Dissertations / Theses on the topic 'Recursive partial least squares'

Partial Least Squares (PLS) has been shown to be a versatile regression technique with an increasing number of applications in the areas of process control, process monitoring and process analysis. This Thesis considers the area of nonlinear PLS; a nonlinear projection based regression technique. The nonlinearity is introduced as a univariate nonlinear function between projections, or to be more specific, linear combinations of the predictor and the response variables. As for the linear case, the method should handle multicollinearity, underdetermined and noisy systems. Although linear PLS is accepted as an empirical regression method, none of the published nonlinear PLS algorithms have achieved widespread acceptance. This is confirmed from a literature survey where few real applications of the methodology were found. This Thesis investigates two nonlinear PLS methodologies, in particular focusing on their limitations. Based on these studies, two nonlinear PLS algorithms are proposed. In the first of the two existing approaches investigated, the projections are updated by applying an optimization method to reduce the error of the nonlinear inner mapping. This ensures that the error introduced by the nonlinear inner mapping is minimized. However, the procedure is limited as a consequence of problems with the nonlinear optimisation. A new algorithm, Nested PLS (NPLS), is developed to address these issues. In particular, a separate inner PLS is used to update the projections. The NPLS algorithm is shown to outperform existing algorithms for a wide range of regression problems and has the potential to become a more widely accepted nonlinear PLS algorithm than those currently reported in the literature. In the second of the existing approaches, the projections are identified by examining each variable independently, as opposed to minimizing the error of the nonlinear inner mapping directly. Although the approach does not necessary identify the underlying functional relationship, the problems of overfitting and other problems associated with optimization are reduced. Since the underlying functional relationship may not be established accurately, the reliability of the nonlinear inner mapping will be reduced. To address this problem a new algorithm, the Reciprocal Variance PLS (RVPLS), is proposed. Compared with established methodology, RVPLS focus more on finding the underlying structure, thus reducing the difficulty of finding an appropriate inner mapping. RVPLS is shown to perform well for a number of applications, but does not have the wide-ranging performance of Nested PLS.

The matrix-inversion-lemma based recursive least squares (RLS) approach is of a recursive form and free of matrix inversion, and has excellent performance regarding computation and memory in solving the classic least-squares (LS) problem. It is important to generalize RLS for generalized LS (GLS) problem. It is also of value to develop an efficient initialization for any RLS algorithm. In Chapter 2, we develop a unified RLS procedure to solve the unconstrained/linear-equality (LE) constrained GLS. We also show that the LE constraint is in essence a set of special error-free observations and further consider the GLS with implicit LE constraint in observations (ILE-constrained GLS). Chapter 3 treats the RLS initialization-related issues, including rank check, a convenient method to compute the involved matrix inverse/pseudoinverse, and resolution of underdetermined systems. Based on auxiliary-observations, the RLS recursion can start from the first real observation and possible LE constraints are also imposed recursively. The rank of the system is checked implicitly. If the rank is deficient, a set of refined non-redundant observations is determined alternatively. In Chapter 4, base on [Li07], we show that the linear minimum mean square error (LMMSE) estimator, as well as the optimal Kalman filter (KF) considering various correlations, can be calculated from solving an equivalent GLS using the unified RLS. In Chapters 5 & 6, an approach of joint state-and-parameter estimation (JSPE) in power system monitored by synchrophasors is adopted, where the original nonlinear parameter problem is reformulated as two loosely-coupled linear subproblems: state tracking and parameter tracking. Chapter 5 deals with the state tracking which determines the voltages in JSPE, where dynamic behavior of voltages under possible abrupt changes is studied. Chapter 6 focuses on the subproblem of parameter tracking in JSPE, where a new prediction model for parameters with moving means is introduced. Adaptive filters are developed for the above two subproblems, respectively, and both filters are based on the optimal KF accounting for various correlations. Simulations indicate that the proposed approach yields accurate parameter estimates and improves the accuracy of the state estimation, compared with existing methods.

CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICO<br>Muitos problemas da área de aprendizagem automática tem por objetivo modelar a complexa relação existente num sisitema , entre variáveis de entrada X e de saída Y na ausência de um modelo teórico. A regressão por mínimos quadrados parciais PLS ( Partial Least Squares) constitui um método linear para resolução deste tipo de problema , voltado para o caso de um grande número de variáveis de entrada quando comparado com número de amostras. Nesta tese , apresentamos uma variante do algoritmo clássico PLS para o tratamento de grandes conjuntos de dados , mantendo um bom poder preditivo. Dentre os principais resultados destacamos um versão paralela PPLS (Parallel PLS ) exata para o caso de apenas um variável de saída e um versão rápida e aproximada DPLS (DIRECT PLS) para o caso de mais de uma variável de saída. Por outro lado ,apresentamos também variantes para o aumento da qualidade de predição graças à formulação não linear. São elas o LPLS ( Lifted PLS ), algoritmo para o caso de apenas uma variável de saída, baseado na teoria de funções de núcleo ( kernel functions ), uma formulação kernel para o DPLS e um algoritmo multi-kernel MKPLS capaz de uma modelagemmais compacta e maior poder preditivo, graças ao uso de vários núcleos na geração do modelo.<br>The purpose of many problems in the machine learning field isto model the complex relationship in a system between the input X and output Y variables when no theoretical model is available. The Partial Least Squares (PLS)is one linear method for this kind of problem, for the case of many input variables when compared to the number of samples. In this thesis we present versions of the classical PLS algorithm designed for large data sets while keeping a good predictive power. Among the main results we highlight PPLS (Parallel PLS), a parallel version for the case of only one output variable, and DPLS ( Direct PLS), a fast and approximate version, for the case fo more than one output variable. On the other hand, we also present some variants of the regression algorithm that can enhance the predictive quality based on a non -linear formulation. We indroduce LPLS (Lifted PLS), for the case of only one dependent variable based on the theory of kernel functions, KDPLS, a non-linear formulation for DPLS, and MKPLS, a multi-kernel algorithm that can result in a more compact model and a better prediction quality, thankas to the use of several kernels for the model bulding.

The inverse kinematics problem for six degree of freedom robots having a separable structure with the wrist equivalent to a spherical joint is considered and an iterative solution based on estimating the inverse Jacobian by recursive least squares estimation is proposed. This solution is found to have properties similar to Wampler's Damped Least Squares method and provides a stable result when the manipulator is in singular regions. Furthermore, the solution is more computationally efficient than Wampler's method; however, its best performance is obtained when the distances between the current end effector pose and the target pose are small. No knowledge of the manipulator's geometry is required provided that the end effector and joint position data are obtained from sensor information. This permits the algorithm to be readily transferable among manipulators and circumvents detailed analysis of the manipulator's structure.<br>Applied Science, Faculty of<br>Electrical and Computer Engineering, Department of<br>Graduate

The design of an application-specific integrated circuit of a parallel array processor is considered for recursive least squares by QR decomposition using Givens rotations, applicable in adaptive filtering and beamforming applications. Emphasis is on high sample-rate operation, which, for this recursive algorithm, means that the time to perform arithmetic operations is critical. The algorithm, architecture and arithmetic are considered in a single integrated design procedure to achieve optimum results. A realisation approach using standard arithmetic operators, add, multiply and divide is adopted. The design of high-throughput operators with low delay is addressed for fixed- and floating-point number formats, and the application of redundant arithmetic considered. New redundant multiplier architectures are presented enabling reductions in area of up to 25%, whilst maintaining low delay. A technique is presented enabling the use of a conventional tree multiplier in recursive applications, allowing savings in area and delay. Two new divider architectures are presented showing benefits compared with the radix-2 modified SRT algorithm. Givens rotation algorithms are examined to determine their suitability for VLSI implementation. A novel algorithm, based on the Squared Givens Rotation (SGR) algorithm, is developed enabling the sample-rate to be increased by a factor of approximately 6 and offering area reductions up to a factor of 2 over previous approaches. An estimated sample-rate of 136 MHz could be achieved using a standard cell approach and O.35pm CMOS technology. The enhanced SGR algorithm has been compared with a CORDIC approach and shown to benefit by a factor of 3 in area and over 11 in sample-rate. When compared with a recent implementation on a parallel array of general purpose (GP) DSP chips, it is estimated that a single application specific chip could offer up to 1,500 times the computation obtained from a single OP DSP chip.

This thesis is concerned with the issue of the regularization of the Recursive Least-Squares (RLS) algorithm. In the first part of the thesis, a novel regularized exponentially weighted array RLS algorithm is developed, which circumvents the problem of fading regularization that is inherent to the standard regularized exponentially weighted RLS formulation, while allowing the employment of generic time-varying regularization matrices. The standard equations are directly perturbed via a chosen regularization matrix; then the resulting recursions are extended to the array form. The price paid is an increase in computational complexity, which becomes cubic. The superiority of the algorithm with respect to alternative algorithms is demonstrated via simulations in the context of adaptive beamforming, in which low filter orders are employed, so that complexity is not an issue. In the second part of the thesis, an alternative criterion is motivated and proposed for the dynamical regulation of regularization in the context of the standard RLS algorithm. The regularization is implicitely achieved via dithering of the input signal. The proposed criterion is of general applicability and aims at achieving a balance between the accuracy of the numerical solution of a perturbed linear system of equations and its distance from the analytical solution of the original system, for a given computational precision. Simulations show that the proposed criterion can be effectively used for the compensation of large condition numbers, small finite precisions and unecessary large values of the regularization.<br>Esta tese trata da regularização do algoritmo dos mínimos-quadrados recursivo (Recursive Least-Squares - RLS). Na primeira parte do trabalho, um novo algoritmo array com matriz de regularização genérica e com ponderação dos dados exponencialmente decrescente no tempo é apresentado. O algoritmo é regularizado via perturbação direta da inversa da matriz de auto-correlação (Pi) por uma matriz genérica. Posteriormente, as equações recursivas são colocadas na forma array através de transformações unitárias. O preço a ser pago é o aumento na complexidade computacional, que passa a ser de ordem cúbica. A robustez do algoritmo resultante ´e demonstrada via simula¸coes quando comparado com algoritmos alternativos existentes na literatura no contexto de beamforming adaptativo, no qual geralmente filtros com ordem pequena sao empregados, e complexidade computacional deixa de ser fator relevante. Na segunda parte do trabalho, um critério alternativo ´e motivado e proposto para ajuste dinâmico da regularização do algoritmo RLS convencional. A regularização é implementada pela adição de ruído branco no sinal de entrada (dithering), cuja variância é controlada por um algoritmo simples que explora o critério proposto. O novo critério pode ser aplicado a diversas situações; procura-se alcançar um balanço entre a precisão numérica da solução de um sistema linear de equações perturbado e sua distância da solução do sistema original não-perturbado, para uma dada precisão. As simulações mostram que tal critério pode ser efetivamente empregado para compensação de números de condicionamento (CN) elevados, baixa precisão numérica, bem como valores de regularização excessivamente elevados.

Partial Least Squares is both a regression method and a tool for variable selection, that is especially appropriate for models based on numerous (possibly correlated) variables. While being a well established modeling tool in chemometrics, this thesis adapts PLS to financial data to predict the movements of the business cycle represented by the OECD Composite Leading Indicators. High-dimensional data is used, and a model with automated variable selection through a genetic algorithm is developed to forecast different economic regions with good results in out-of-sample tests.<br>Partial Least Squares är både en regressionsmetod och ett verktyg för variabelselektion som är specielltlämpligt för modeller baserade på en stor mängd (möjligtvis korrelerade) variabler.Medan det är en väletablerad modelleringsmetod inom kemimetri, anpassar den häruppsatsen PLS till finansiell data för att förutspå rörelserna av konjunkturen,representerad av OECD's Composite Leading Indicator. Högdimensionella dataanvänds och en model med automatiserad variabelselektion via en genetiskalgoritm utvecklas för att göra en prognos av olika ekonomiska regioner medgoda resultat i out-of-sample-tester

Thesis (MComm (Statistics and Actuarial Science))--University of Stellenbosch, 2009.<br>When determining the chemical composition of a specimen, traditional laboratory techniques are often both expensive and time consuming. It is therefore preferable to employ more cost effective spectroscopic techniques such as near infrared (NIR). Traditionally, the calibration problem has been solved by means of multiple linear regression to specify the model between X and Y. Traditional regression techniques, however, quickly fail when using spectroscopic data, as the number of wavelengths can easily be several hundred, often exceeding the number of chemical samples. This scenario, together with the high level of collinearity between wavelengths, will necessarily lead to singularity problems when calculating the regression coefficients. Ways of dealing with the collinearity problem include principal component regression (PCR), ridge regression (RR) and PLS regression. Both PCR and RR require a significant amount of computation when the number of variables is large. PLS overcomes the collinearity problem in a similar way as PCR, by modelling both the chemical and spectral data as functions of common latent variables. The quality of the employed reference method greatly impacts the coefficients of the regression model and therefore, the quality of its predictions. With both X and Y subject to random error, the quality the predictions of Y will be reduced with an increase in the level of noise. Previously conducted research focussed mainly on the effects of noise in X. This paper focuses on a method proposed by Dardenne and Fernández Pierna, called Noise Addition Partial Least Squares (NAPLS) that attempts to deal with the problem of poor reference values. Some aspects of the theory behind PCR, PLS and model selection is discussed. This is then followed by a discussion of the NAPLS algorithm. Both PLS and NAPLS are implemented on various datasets that arise in practice, in order to determine cases where NAPLS will be beneficial over conventional PLS. For each dataset, specific attention is given to the analysis of outliers, influential values and the linearity between X and Y, using graphical techniques. Lastly, the performance of the NAPLS algorithm is evaluated for various

Includes bibliographical references.<br>In multivariate analysis, data matrices are often very large, which sometimes makes it difficult to describe their structure and to make a visual inspection of the relationship between their respective rows (samples) and columns (variables). For this reason, biplots, the joint graphical display of the rows and columns of a data matrix, can be useful tools for analysis. Since they were first introduced, biplots have been employed in a number of multivariate methods, such as Correspondence Analysis (CA), Principal Component Analysis (PCA), Canonical Variate Analysis (CVA) and Discriminant Analysis (DA), as a form of graphical display of data. Another possible employment is in Partial Least Squares (PLS). First introduced as a regression method, PLS is more flexible than multivariate regression, but better suited than Principal Component Regression (PCR) for the prediction of a set of response variables from a large set of predictor variables. Employing the biplot in PLS gave rise to the PLS biplot, a new addition to the biplot family. In the current study, this biplot was successfully applied to the sensory data to investigate the relationships between the sensory panel characteristics and the chemical quality measurements of sixteen olive oils. It was also applied to a large set of mineral sorting production data to investigate the relationships between the output variables and the process factors used to produce a final product. Furthermore, the PLS biplot was applied to a Binomialdistributed data concerning the diabetes testing of Indian women and to a Poisson-distributed data showing the diversity of arboreal marsupials (possum) in the Montane ash forest. After these applications, it is proposed that the PLS biplot is a useful graphical tool for displaying results from the (univariate) Partial Least Squares-Generalized Linear Model (PLS-GLM) analysis of a data set. With Partial Least Squares Regression (PLSR) being a valuable method for modelling high-dimensional data, especially in chemometrics, the PLS biplot was successfully applied to a cereal evaluation containing one hundred and forty five infrared spectra and six chemical properties, and a gene expression data with two thousand genes.

A recursive least-squares algorithm was developed to estimate respiratory mechanical parameters with high temporal resolution. This algorithm was used to investigate the time course of bronchoconstriction induced by intravenous histamine injection in the dog. The onset of the response of lung tissue resistance and elastance demonstrated a different time course than airway resistance. This was interpreted in terms of the sequential delivery of the drug first through the pulmonary and then the bronchial circulations. The time course of respiratory mechanical parameters among various alveolar capsules revealed two patterns of inhomogeneity development. The first one was random whereas the second one was progressive with dose. A mathematical derivation elucidated the negative tissue resistance frequently obtained at high levels of constriction. The time courses of respiratory resistance and elastance during bronchoconstriction were transient and scaled with dose. They were reproducible for repeated doses of histamine after indomethacin pre-treatment and were intrinsically modulated by the adrenergic sympathetic system and through the $ rm H sb2$ histamine receptors.

Adaptive filters have found applications in many signal processing problems. In some situations, linear constraints are imposed on the filter weights such that the filter is forced to exhibit a certain desired response. Several algorithms for linearly constrained least-squares adaptive filtering have been developed in the literature. When implemented with finite precision arithmetic, these algorithms are inevitably subjected to rounding errors. It is essential to understand how these algorithms react to rounding errors.In this thesis, the numerical properties of three linearly constrained least-squares adaptive filtering algorithms, namely, the linearly constrained fast least algorithm, the linear systolic array for MVDR beamforming and the linearly constrained QRD-RLS algorithm, are studied. It is shown that all these algorithms can be separated into a constrained part and an unconstrained part. The numerical properties of unconstrained least-squares algorithms (i.e., the unconstrained part of the linearly constrained algorithms under study) are reviewed from the perspectives of error propagation, error accumulation and numerical persistency. It is shown that persistent excitation and sufficient numerical resolution are needed to ensure the stability of the CRLS algorithm, while the QRD-RLS algorithm is unconditionally stable. The numerical properties of the constrained algorithms are then examined. Based on the technique of how the constraints are applied, these algorithms can be grouped into two categories. The first two algorithms admit a similar structure in that the unconstrained parts preceed the constrained parts. Error propagation analysis shows that this structure gives rise to unstable error propagation in the constrained part. In contrast, the constrained part of the third algorithm preceeds the unconstrained part. It is shown that this algorithm gives an exact solution to a linearly constrained least-squares adaptive filtering problem with perturbed constraints and perturbed input data. A minor modification to the constrained part of the linearly constrained QRD-RLS algorithm is proposed to avoid a potential numerical difficulty due to the Gaussian elimination operation employed in the algorithm.

Adaptive filters have found applications in many signal processing problems. In some situations, linear constraints are imposed on the filter weights such that the filter is forced to exhibit a certain desired response. Several algorithms for linearly constrained least-squares adaptive filtering have been developed in the literature. When implemented with finite precision arithmetic, these algorithms are inevitably subjected to rounding errors. It is essential to understand how these algorithms react to rounding errors.In this thesis, the numerical properties of three linearly constrained least-squares adaptive filtering algorithms, namely, the linearly constrained fast least algorithm, the linear systolic array for MVDR beamforming and the linearly constrained QRD-RLS algorithm, are studied. It is shown that all these algorithms can be separated into a constrained part and an unconstrained part. The numerical properties of unconstrained least-squares algorithms (i.e., the unconstrained part of the linearly constrained algorithms under study) are reviewed from the perspectives of error propagation, error accumulation and numerical persistency. It is shown that persistent excitation and sufficient numerical resolution are needed to ensure the stability of the CRLS algorithm, while the QRD-RLS algorithm is unconditionally stable. The numerical properties of the constrained algorithms are then examined. Based on the technique of how the constraints are applied, these algorithms can be grouped into two categories. The first two algorithms admit a similar structure in that the unconstrained parts preceed the constrained parts. Error propagation analysis shows that this structure gives rise to unstable error propagation in the constrained part. In contrast, the constrained part of the third algorithm preceeds the unconstrained part. It is shown that this algorithm gives an ++<br>exact solution to a linearly constrained least-squares adaptive filtering problem with perturbed constraints and perturbed input data. A minor modification to the constrained part of the linearly constrained QRD-RLS algorithm is proposed to avoid a potential numerical difficulty due to the Gaussian elimination operation employed in the algorithm.

Multivariate statistical modelling and monitoring is an active area of research and development in both academia and industry. This is due to the economic and safety benefits that can be attained from the implementation of process modelling and monitoring schemes. Most industrial processes in the chemistry-using sector exhibit complex characteristics including process dynamics, non-linearity and changes in operational behaviour which are compounded by the occurrence of non-conforming data points. To date, modelling and monitoring methodologies have focussed on processes exhibiting one of the aforementioned characteristics. This Thesis considers the development and application of multivariate statistical methods for the modelling and monitoring of the whole process as well as individual unit operations with a particular focus on the complex dynamic nonlinear behaviour of continuous processes. Following a review of Partial Least Squares (PLS), which is applicable for the analysis of problems that exhibit high dimensionality and correlated/collinear variables, it was observed that it is inappropriate for the analysis of data from complex dynamic processes. To address this issue, a multivariate statistical method Robust Adaptive PLS (RAPLS) was proposed, which has the ability to distinguish between non-conforming data, i.e. statistical outliers and a process fault. Through the analysis of data from a mathematical simulation of a time varying and non-stationary process, it is observed that RAPLS shows superior monitoring performance compared to conventional PLS. The model has the ability to adapt to changes in process operating conditions without losing its ability to detect process faults and statistical outliers. A dynamic extension, RADPLS, using an autoregressive with exogenous inputs (ARX) representation was developed to model and monitor the complex dynamic and nonlinear behaviour of an Ammonia Synthesis Fixed-bed Reactor. The resultant model, which is resistant to outliers, shows significant improvement over other dynamic PLS based representations. The proposed method shows some limitations in terms of the detection of the fault for its full duration but it significantly reduces the false alarm rate. The RAPLS algorithm is further extended to a dynamic multi-block algorithm, RAMBDPLS, through the conjunction of a finite impulse response (FIR) representation and multiblock PLS. It was applied to the benchmark Tennessee Eastman Process to illustrate its applicability for the monitoring of the whole process and individual unit operations and to demonstrate the concept of fault propagation in a dynamic and nonlinear continuous system. The resulting model detects the faults and reduces the false alarm rate compared to conventional PLS.

High-dimensional data sets with a large number of explanatory variables are increasingly important in applications of regression analysis. It is well known that most traditional statistical techniques, such as the Ordinary Least Square (OLS) estimation do not perform well with such data and are either ill-conditioned or undefined. Thus a need for regularization arises. In the literature, various regularization methods have been suggested; amongst the most famous is the Partial Least Squares (PLS) regression method. The aim of this thesis is to consolidate and extend results in the literature to (a) show that PLS estimation can be regarded as estimation under a statistical model based on the so-called “Krylov hypothesis”, (b) introduce a derivation of the PLS estimator as an approximate maximum likelihood estimator under this model and (c) propose an algorithm to modify the PLS estimator to yield an exact maximum likelihood estimator under the same model. It will be shown that the constrained optimization problem in (c) can be recast as an unconstrained optimization problem on the Grassmann manifold. Two simulation studies consisting of a number of examples (using artificial data) in low dimensions will be presented. These allow us to make a visual inspection of the Krylov maximum likelihood as it varies over the Grassmann manifolds and hence characteristics of the data for which KML can be expected to give better results than PLS can be identified. However it was observed that these ideas make sense only when there is a small number of explanatory variables. As soon as the number of explanatory variables is moderate (say p = 10) or of order thousands, exploring how the different parameters effect the behaviour of the objective function is not straight forward. The predictive ability of the Ordinary Least Squares (OLS), Partial Least Squares (PLS) and Krylov Maximum Likelihood (KML) regression methods when applied to artificial data (for which the sample size is bigger than the number of explanatory variables) with and without multicollinearity is explored. Finally the predictive ability of the Partial Least Squares (PLS) and Krylov Maximum Likelihood (KML) regression methods was also compared on two real life high-dimensional data sets from the literature.

Algorithms have been developed which perform least squares adaptive filtering with great computational efficiency. Unfortunately, the fast recursive least squares (RLS) algorithms all exhibit numerical instability due to finite precision computational errors, resulting in their failure to produce a useful solution after a short number of iterations. In this thesis, a new solution to this instability problem is considered, making use of interval arithmetic. By modifying the algorithm so that upper and lower bounds are placed on all quantities calculated, it is possible to obtain a measure of confidence in the solution calculated by a fast RLS algorithm and if it is subject to a high degree of inaccuracy due to finite precision computational errors, then the algorithm may be rescued, using a reinitialisation procedure. Simulation results show that the stabilised algorithms offer an accuracy of solution comparable with the standard recursive least squares algorithm. Both floating and fixed point implementations of the interval arithmetic method are simulated and long-term stability is demonstrated in both cases. A hardware verification of the simulation results is also performed, using a digital signal processor(DSP). The results from this indicate that the stabilised fast RLS algorithms are suitable for a number of applications requiring high speed, real time adaptive filtering. A design study for a very large scale integration (VLSI) technology coprocessor, which provides hardware support for interval multiplication, is also considered. This device would enable the hardware realisation of a fast RLS algorithm to operate at far greater speed than that obtained by performing interval multiplication using a DSP. Finally, the results presented in this thesis are summarised and the achievements and limitations of the work are identified. Areas for further research are suggested.

Lineare Modelle mit latenten Variablen sind seit langem verbreitete Analyse- und Prognoseinstrumente in den Sozialwissenschaften. Auch in der Ökonometrie gibt es einige Anwendungen. Die meistverbreiteten Modellierungs- und Schätzverfahren sind LISREL von Jöreskog und Sörbom (z.B. 1987) und Partial Least Squares (PLS) von H. Wold (1973). Während LISREL mehr modellorientiert und in der Anwendung konfirmativ ist, kann man PLS als datenorientiert und eher deskriptiv oder explorativ bezeichnen. Charakteristisch für Wolds Herangehen ist, daß das PLS-Modell eigentlich nur durch den Algorithmus zu seiner Schätzung definiert wird. Das umfassendste Programmsystem für PLS ist LVPLS von J. B. Lohmöller (1984). Es lehnt sich sehr eng an die Theorie von Wold an und ist trotz mangelnden Nutzerkomforts in seiner Vielseitigkeit und Zuverlässigkeit unübertroffen. Weder Wolds Verfahren noch Lohmöllers Programm sehen die Anwendung auf dynamische Modelle, etwa VARs, explizit vor. Die Einbeziehung verzögerter Variablen ist nur in Form selbständiger Variablen möglich, was zu Inkonsistenzen bei der Gewichtung führt. Im folgenden zweiten Abschnitt wird ein Verfahren skizziert (vgl. Strohe 1995), das sich einerseits sehr eng an den Woldschen Algorithmus anlehnt, das aber andererseits speziell auf die Behandlung von dynamischen Modellen mit verzögerten latenten Variablen ausgerichtet ist. Der dritte Abschnitt bringt dann eine Einführung in das entsprechende ISP™ Computerprogramm DPLS (vgl. Geppert 1995). Er besteht aus einer allgemeinen Programmbeschreibung und einer detaillierten Nutzeranleitung. Hinzu kommt die Bearbeitung eines kleinen ökonometrischen Demonstrationsmodells. Im vierten Abschnitt werden mit einer Simulationsstudie die Eigenschaften des Schätzverfahrens DPLS unter verschiedenen Verteilungsannahmen geprüft. Der Anhang bringt die vollständigen Listings der kommentierten Programm-Macros.

Dans cette thèse, nous comparons les prévisions IMS, DMS et PLS à plusieurs horizons, en nous concentrant sur les propriétés combinatoires des PLS. Nous nous appuyons sur un article intéressant de Franses &amp; Legerstee (2010), qui suggère comment la méthode dite des moindres carrés partiels (PLS) peut être considérée, dans le contexte de la prévision sur plusieurs étapes, comme une technique intermédiaire entre IMS et DMS. En fait, plutôt qu’un «intermédiaire», nous aimons considérer le PLS comme une forme de combinaison de IMS et de DMS.Cette thèse comprend quatre chapitres.Au chapitre 1, nous fournissons une revue de la littérature qui sert de contexte aux chapitres suivants. Ce chapitre sert de motivation pour les analyses ultérieures.Au chapitre 2, nous explorons les fonctionnalités de PLS considérées comme une combinaison d'IMS et de DMS. Nous étudions les propriétés de PLS en utilisant un algorithme suggéré par Garthwaite (1994).Nous étudions la relation entre IMS, DMS et PLS et comparons la précision de leurs prévisions à plusieurs horizons. Nous analysons les propriétés combinatoires de PLS dans la prévision en plusieurs étapes à l'aide d'un modèle simple AR (2). Pour comparer les performances de prévision, nous évaluons leurs propriétés asymptotiques sous des modèles bien spécifiés et mal spécifiés. Nous confirmons notre étude analytique par le biais de simulations approfondies de la précision relative de la prévision des différentes techniques de prévision à plusieurs étapes. A travers ces simulations, nous soutenons l'analyse asymptotique et étudions les conditions qui rendent le PLS meilleur que l'IMS ou le DMS.Au chapitre 3, nous menons une étude empirique de la prévision en plusieurs étapes basée sur des modèles de AR univariés et nous nous concentrons sur les 121 séries chronologiques mensuelles macroéconomiques aux États-Unis.Nous fournissons une analyse empirique visant à déterminer les circonstances qui rendent PLS préférable à IMS ou à DMS. Pour une comparaison plus facile avec la littérature, nous suivons Marcellino et al. (2006) et McCracken &amp; McGillicuddy (2019) à bien des égards. En outre, nous étendons leurs résultats dans certaines directions, telles que l’évaluation de la prévision de trajectoire, les techniques de mesure alternatives et différents sous-échantillons.Nous explorons les avantages en relation avec la persistance de la série mesurée par le degré d'intégration fractionnaire.A travers cette analyse empirique, nous reconfirmons les résultats des études précédentes et découvrons plusieurs faits nouveaux: (i) les avantages relatifs du PLS par rapport au système IMS ont tendance à disparaître à mesure que l'horizon de prévision se développe; (ii) le PLS est généralement meilleur lorsque le modèle utilise des décalages courts; et (iii) les PLS fonctionnent mieux que le système IMS lorsque les données subissent des périodes de forte volatilité.Le dernier chapitre étend le chapitre 3 aux modèles multivariés. Nous comparons une brève étude analytique de la raison d'être du PLS, puis comparons de manière empirique les performances de prévision du SGI, du IMS et du DMS dans le contexte de modèles de prévision à deux variables. Pour chaque modèle de prévision, nous produisons et évaluons des prévisions sur un seul horizon et sur des trajectoires (plages d'horizons). Nos résultats confirment ceux des modèles univariés: la PLS est privilégiée à court terme mais la question cruciale concerne la persistance des données. À cet égard, les données relatives au groupe des prix nominaux, des salaires et de la monnaie font apparaître une forme de persistance qui ne suit pas clairement une tendance I (1) ou I (2) et produit des performances PLS bien supérieures. Globalement, nous trouvons également que le PLS est génériquement préféré au DMS, il devrait donc constituer une alternative pour le praticien chaque fois qu’il peut envisager des techniques de prévision directe<br>In this thesis, we compare IMS, DMS, and PLS forecasts at several horizons, focusing on the combinational properties of PLS.We build upon an interesting article by Franses &amp; Legerstee (2010) who suggest how the method called Partial Least Squares (PLS) can be seen, in the context of multistep forecasting, as an intermediate technique between IMS and DMS.In fact, rather than an ‘intermediate’, we like to see PLS as a form of combination of IMS and DMS.This thesis consists of four chapters.In the first chapter, we provide a review of the literature serves as the context for the following chapters. In particular, we provide definitions for IMS and DMS and discuss the literature which compares them theoretically and empirically. We then move to forecasting combination and also provide a motivation for seeing PLS as a combination between IMS and DMS. This is where we discuss in details some of features of PLS, such as e.g. its origins, competing algorithms and properties. We also provide a comparison with related methods. The chapter serves as a motivation for the subsequent analyses.In Chapter 2, we explore features of PLS seen as a combination of IMS and DMS. We investigate the properties of PLS using an algorithm suggested by Garthwaite (1994).We study the relationship between IMS, DMS, and PLS, and compare their forecast accuracy at several horizons. We analyze the combinational properties of PLS in multistep forecasting using a simple AR(2) model. To compare forecasting performances, we evaluate their asymptotic properties under well- and misspecified models. We confirm our analytical study through an extensive simulations of the relative forecast accuracy of the various multistep forecasting techniques. Through these simulations, we support the asymptotic analysis and study the conditions which render PLS better than IMS or DMS.(These results enable us to revisit the motivating article by Franses &amp; Legerstee (2010).)In Chapter 3, we conduct an extensive empirical study of multistep forecasting based on univariate AR models and focus on the 121 monthly US macroeconomic time series.We provide an empirical analysis which aims to determine the circumstances that make PLS preferable to IMS or DMS. For an easier comparison with the literature, we follow Marcellino et al. (2006) and McCracken &amp; McGillicuddy (2019) in many aspects. In addition, we extend their results in some directions, such as path forecasting evaluation, alternative measurement techniques, and different subsamples.We explore the benefits in relation to the persistence of the series measured by the degree of fractional integration.Through this empirical analysis we reconfirm the results of the previous studies and find several new facts: (i) the relative benefits of PLS over IMS tend to vanish as the forecast horizon grows; (ii) PLS is in general better when the model uses short lags; and (iii) PLS performs better than IMS when the data undergoes periods of high volatility.The last chapter extends Chapter 3 to multivariate models. We compare a short analytical study of the rationale for PLS and then compare empirically the forecasting performances of IMS, DMS, and PLS in the context of bivariate forecasting models. For each forecasting model, we produce and assess single-horizon and path (ranges of horizons) forecasts. Our findings confirm those of the univariate models: PLS is preferred at short horizons but the issue that is crucial concerns the persistence of the data. In this respect, the data that pertains to the group of nominal prices, wages and money exhibit a form of persistence that does not follow clear an I(1) or an I(2) trend and yield much superior PLS performances. Overall, we also find that PLS is generically preferred to DMS so it should constitute an alternative for the practitioner whenever she may consider direct forecasting techniques

Kernel-based meshless methods for approximating functions and solutions of partial differential equations have many applications in engineering fields. As only scattered data are used, meshless methods using radial basis functions can be extended to complicated geometry and high-dimensional problems. In this thesis, kernel-based least-squares methods will be used to solve several direct and inverse problems. In chapter 2, we consider discrete least-squares methods using radial basis functions. A general l^2-Tikhonov regularization with W_2^m-penalty is considered. We provide error estimates that are comparable to kernel-based interpolation in cases in which the function being approximated is within and is outside of the native space of the kernel. These results are extended to the case of noisy data. Numerical demonstrations are provided to verify the theoretical results. In chapter 3, we apply kernel-based collocation methods to elliptic problems with mixed boundary conditions. We propose some weighted least-squares formulations with different weights for the Dirichlet and Neumann boundary collocation terms. Besides fill distance of discrete sets, our weights also depend on three other factors: proportion of the measures of the Dirichlet and Neumann boundaries, dimensionless volume ratios of the boundary and domain, and kernel smoothness. We determine the dependencies of these terms in weights by different numerical tests. Our least-squares formulations can be proved to be convergent at the H^2 (Ω) norm. Numerical experiments in two and three dimensions show that we can obtain desired convergent results under different boundary conditions and different domain shapes. In chapter 4, we use a kernel-based least-squares method to solve ill-posed Cauchy problems for elliptic partial differential equations. We construct stable methods for these inverse problems. Numerical approximations to solutions of elliptic Cauchy problems are formulated as solutions of nonlinear least-squares problems with quadratic inequality constraints. A convergence analysis with respect to noise levels and fill distances of data points is provided, from which a Tikhonov regularization strategy is obtained. A nonlinear algorithm is proposed to obtain stable solutions of the resulting nonlinear problems. Numerical experiments are provided to verify our convergence results. In the final chapter, we apply meshless methods to the Gierer-Meinhardt activator-inhibitor model. Pattern transitions in irregular domains of the Gierer-Meinhardt model are shown. We propose various parameter settings for different patterns appearing in nature and test these settings on some irregular domains. To further simulate patterns in reality, we construct different kinds of domains and apply proposed parameter settings on different patches of domains found in nature.

Der statistische Diskussionbeitrag untersucht, ob und wie sich Erwartungen und Stimmungen in der Wirtschaft bilden bzw. von welchen volkswirtschaftlichen Größen sie abhängen. Als Methodik werden Partial Least Squares (PLS) Modelle genutzt, eine Modellklasse der Pfadanalyse mit latenten Variablen. Die verwendeten Daten wurden vom Ifo-Institut und aus der amtlichen Statistik entnommen.<br>This paper analyses the development of sentiments and expectations in the German economy. The issue is how these expectatons are influenced by major macroeconomic variables like investments or unemployment. Several Partial Least Squares models (PLS) are used to estimate the relations. The data is derived from the German Ifo Institut and the official statistic.

In this thesis, we consider the problem of constructing an additive risk model based on the right censored survival data to predict the survival times of the cancer patients, especially when the dimension of the covariates is much larger than the sample size. For microarray Gene Expression data, the number of gene expression levels is far greater than the number of samples. Such ¡°small n, large p¡± problems have attracted researchers to investigate the association between cancer patient survival times and gene expression profiles for recent few years. We apply Partial Least Squares to reduce the dimension of the covariates and get the corresponding latent variables (components), and these components are used as new regressors to fit the extensional additive risk model. Also we employ the time dependent AUC curve (area under the Receiver Operating Characteristic (ROC) curve) to assess how well the model predicts the survival time. Finally, this approach is illustrated by re-analysis of the well known AML data set and breast cancer data set. The results show that the model fits both of the data sets very well.

Principal components regression (PCR) and partial least squares regression (PLS) are widely used in multivariate calibration in the fields of chemometrics, econometrics, social science and so forth, serving as alternative solutions to the problems which arise in ordinary least squares regression when explanatory variables are either collinear, or there are hundreds of explanatory variables with a relatively small sample size. Both PCR and PLS tackle the problems by constructing lower dimensional factors based on the explanatory variables. The extra step of factor construction makes the standard prediction uncertainty theory of ordinary least squares regression not directly applicable to the two reduced dimension methods. In the thesis, we start by reviewing the ordinary least squares regression prediction uncertainty theory, and then investigate how the theory performs when it extends to PCR and PLS, aiming at potentially better approaches. The first main contribution of the thesis is to clarify the quantification of prediction uncertainty for PLS. We rephrase existing methods with consistent mathematical notations in the hope of giving a clear guidance to practitioners. The second main contribution is to develop a new linearisation method for PLS. After establishing the theory, simulation and real data studies have been employed to understand and compare the new method with several commonly used methods. From the studies of simulations and a real dataset, we investigate the properties of simple approaches based on the theory of ordinary least squares theory, the approaches using resampling of data, and the local linearisation approaches including a classical and our improved new methods. It is advisable to use the ordinary least squares type prediction variance with the estimated regression error variance from the tuning set in both PCR and PLS in practice.

Doctor of Philosophy (PhD)<br>This thesis considers transmission techniques for current and future wireless and mobile communications systems. Many of the results are quite general, however there is a particular focus on code-division multiple-access (CDMA) and multi-input multi-output (MIMO) systems. The thesis provides analytical techniques and results for finding key performance metrics such as signal-to-interference and noise power ratios (SINR) and capacity. This thesis considers a large-system analysis of a general linear matrix-vector communications channel, in order to determine the asymptotic performance of linear fixed and adaptive receivers. Unlike many previous large-system analyses, these results cannot be derived directly from results in the literature. This thesis considers a first-principles analytical approach. The technique unifies the analysis of both the minimum-mean-squared-error (MMSE) receiver and the adaptive least-squares (ALS) receiver, and also uses a common approach for both random i.i.d. and random orthogonal precoding. The approach is also used to derive the distribution of sums and products of free random matrices. Expressions for the asymptotic SINR of the MMSE receiver are derived, along with the transient and steady-state SINR of the ALS receiver, trained using either i.i.d. data sequences or orthogonal training sequences. The results are in terms of key system parameters, and allow for arbitrary distributions of the power of each of the data streams and the eigenvalues of the channel correlation matrix. In the case of the ALS receiver, we allow a diagonal loading constant and an arbitrary data windowing function. For i.i.d. training sequences and no diagonal loading, we give a fundamental relationship between the transient/steady-state SINR of the ALS and the MMSE receivers. We demonstrate that for a particular ratio of receive to transmit dimensions and window shape, all channels which have the same MMSE SINR have an identical transient ALS SINR response. We demonstrate several applications of the results, including an optimization of information throughput with respect to training sequence length in coded block transmission.

This thesis considers transmission techniques for current and future wireless and mobile communications systems. Many of the results are quite general, however there is a particular focus on code-division multiple-access (CDMA) and multi-input multi-output (MIMO) systems. The thesis provides analytical techniques and results for finding key performance metrics such as signal-to-interference and noise power ratios (SINR) and capacity. This thesis considers a large-system analysis of a general linear matrix-vector communications channel, in order to determine the asymptotic performance of linear fixed and adaptive receivers. Unlike many previous large-system analyses, these results cannot be derived directly from results in the literature. This thesis considers a first-principles analytical approach. The technique unifies the analysis of both the minimum-mean-squared-error (MMSE) receiver and the adaptive least-squares (ALS) receiver, and also uses a common approach for both random i.i.d. and random orthogonal precoding. The approach is also used to derive the distribution of sums and products of free random matrices. Expressions for the asymptotic SINR of the MMSE receiver are derived, along with the transient and steady-state SINR of the ALS receiver, trained using either i.i.d. data sequences or orthogonal training sequences. The results are in terms of key system parameters, and allow for arbitrary distributions of the power of each of the data streams and the eigenvalues of the channel correlation matrix. In the case of the ALS receiver, we allow a diagonal loading constant and an arbitrary data windowing function. For i.i.d. training sequences and no diagonal loading, we give a fundamental relationship between the transient/steady-state SINR of the ALS and the MMSE receivers. We demonstrate that for a particular ratio of receive to transmit dimensions and window shape, all channels which have the same MMSE SINR have an identical transient ALS SINR response. We demonstrate several applications of the results, including an optimization of information throughput with respect to training sequence length in coded block transmission.

Two general goals were raised in this thesis: First, to establish a PLS model for patent value and to investigate causality relationships among variables that determine the patent value; second, to investigate the performance of Partial Least Squares (PLS) Path Modelling with Mode C inthe context of patent value models. This thesis is organized in 10 chapters. Chapter 1 presents an introduction to the thesis that includes the objectives, research scope and the document’s structure. Chapter 2 gives an overview of the different approaches for patent value from the perspective of technological change. Definitions related to patent documents and patent indicators are provided. Chaper 3 reports on patent sample descriptions. We present criteria to retrieve data, the procedure for calculating patent indicators, and a statistical data description. Chapter 4 provides an introduction to structural equation models (SEMs) including origins, basic background and recent developments. In addition, it provides guidelines for model specification and modelling process for SEMs. Special emphasis is placed on determining the reflective or formative nature of measurement models. Chapter 5 puts forward the main PLS algorithms: NIPALS, PLS Regression and PLS Path Modelling. We present two path modelling implementations: Lohmöller and Wold’s procedures. Additionally, insights are given on procedure sensitivity to starting weight values and weighting schemes; algorithm properties, such as consistency and consistency at large; and convergence. We briefly review some PLS Path Modelling extensions and relationships with other procedures. The chapter ends by describing validation techniques. Chapter 6 provides evidence about the accuracy and precision of PLS Path Modelling with Mode C to recover true values in SEMs with few indicators per construct. Monte Carlo simulations and computational experiments are carried out to study the performance of the algorithm. Chapter 7 addresses the formulation and estimation of patent value models. This entails the identification and definition of observable and unobservable variables, the determination of blocks of manifest variables and structural relationships, the specification of a first- and a second-order models of patent value, and the models’ estimation by PLS Path Modelling. In Chapter 8, the evolution of patent value over time using longitudinal SEMs is investigated. Two set-ups are explored. The first longitudinal model includes time-dependent manifest variables and the second includes time-dependent unobservable variables. The SEMs are estimated using PLS Path Modelling. In Chapter 9, there is a description of a Two-Step PLS Path Modelling with Mode C (TsPLS) procedure to study nonlinear and interaction effects among formative constructs. Monte Carlo simulations are performed to generate data and to determine the accuracy and precision of this approach to recover true values. This chapter includes an application of the TsPLS algorithm to patent value models. Finally, in Chapter 10, we provide a summary of conclusions and future researchs. The main contribution of this thesis is to set-up a PLS model for patent value, and around this issue, we have also contributed in two main areas: Contributions to the field of Technological Change are comprised of: (1) Evidence on the role of the knowledge stock, technological scope and international scope as determinants of patent value and technological usefulness. A stable pattern of path coefficients was found across samples in different time periods. (2) To conceptualize the patent value as a potential and a recognized value for intangible assets. It was also shown that the potential value of patent is small compared to the value that is given later. (3) Evidence for the importance of considering the longitudinal nature of the indicators in the patent value problem, especially for forward citations, which are the most widely used indicator of patent value. (4) To introduce a multidimensional perspective of the patent valuation problem. This novel approach may offer a robust understanding of the different varia bles that determine patent value. Contributions to the field of PLS Path Modelling are comprised of: (5) Empirical evidence on the performance of PLS Path Modelling with Mode C. If properly implemented, the procedure can adequately capture some of the complex dynamic relationships involved in models. Our research shows that PLS Path Modelling with Mode C performs according to the theoretical framework established for PLS procedures and PLS-models (Wold, 1982; Krämer, 2006; Hanafi, 2007; Dijkstra, 2010). (6) Empirical evidence for the consistency at large of the PLS Path Modelling with Mode A. (7) Empirical evidence for formative outer models with few manifest variables. (8) Empirical evidence on the performance of a Two-Step PLS Path Modelling with Mode C procedure to estimate nonlinear and interaction effects among formative constructs.<br>Dos objetivos general fueron planteados en esta tesis. Primero, establacer un modelo PLS para el valor de las patentes e investigar las relaciones de causalidad entre las variables que determinan el valor de las patentes. Segundo, investigar el desempeño del procedimiento Partial Least Squares (PLS) Path Modelling con Modo C en el contexto de los modelos de valor de las patentes. La tesis es organizada en 10 capítulos. El Capítulo 1 presenta una introducción a la tesis que incluye los objetivos, el alcance de la investigación y la estructura del documento. El Capítulo 2 entrega una presentación general de los diferentes enfoques para valoración de patentes desde una perspectiva del cambio tecnológico. También se entregan las definiciones necesarias relacionadas con los documentos e indicadores de patentes. El Capítulo 3 describe la muestra de patentes usada en esta investigación. Se presentan los criterios utilizados para recuperar los datos, el procedimiento seguido para calcular los indicadores de patentes y la descripción estadística de la muestra. El Capítulo 4 provee una introducción a los modelos de ecuaciones estructurales (SEMs) incluyendo orígenes, antecedentes básicos y desarrollos recientes. Además se entregan los lineamientos para la especificación de los modelos y el proceso de modelamiento para SEMs. Este capítulo discute con especial énfasis la determinación de la naturaleza reflectiva o formativa de los modelos de medida. El Capítulo 5 presenta los principales algoritmos PLS: NIPALS, Regresión PLS y PLS Path Modelling. Se presentan dos implementaciones de PLS Path Modelling: los procedimientos de Lohmöller y Wold. Adicionalmente, se analyzan resultados previos relacionados con: la sensibilidad del procedimiento al valor inicial de los vectores de pesos y el esquema de ponderación, y las propiedades del algoritmo, tales como consistencia, consistencia “at large” y convergencia. También brevemente se revisan algunas extensiones del procedimiento y su relación con otros métodos. El capítulo termina describiendo las técnicas de validación. El Capítulo 6 provee evidencia acerca de la exactitud y precisión con que PLS Path Modelling con Modo C recupera valores verdaderos en SEMs con pocos indicadores por constructo. Simulaciones Monte Carlo y experimentos computacionales son llevados a cabo para estudiar el rendimiento del algoritmo. El Capítulo 7 trata la formulación y estimación de los modelos de valoración de patentes. Esto comprende la identificación y definición de las variables observables y no observables, la determinación de los bloques de variables manifiestas y las relaciones estructurales, la especificación de los modelos de primer y segundo orden del valor de las patentes y la estimación de los mismos con PLS Path Modelling. En el Capítulo 8, la evolución del valor de las patentes a través del tiempo es investigado usando SEMs longitudinales. Dos set-ups son explorados. El primer modelo longitudinal considera variables manifiestas dependientes del tiempo y el segundo incluye variables latentes dependientes del tiempo. Los SEMs son estimados usando PLS Path Modelling. En el Capítulo 9, el procedimiento Two-Step PLS Path Modelling con Modo C (TsPLS) es implementado para estudiar los efectos no lineales y de interacción entre constructos formativos. Simulaciones Monte Carlo son llevadas a cabo para generar datos y determinar la exactitud y precisión con que este enfoque recupera valores verdaderos. Este capítulo incluye una aplicación del procedimiento a los modelos de patentes. Finalmente, el Capítulo 10 provee un resumen de las conclusiones y lineamientos para futuras investigaciones. La principal contribución de esta tesis es proponer modelos PLS para el valor de las patentes, y alrededor de este objetivo, nosotros hemos también contribuido en dos áreas principales: Contribuciones en el área del Cambio Tecnológico comprenden: (1) Evidencia empírica del rol del stock de conocimiento, el alcance tecnológico y el alcance internacional como determinantes del valor de las patentes y la utilidad tecnológica. Un patrón estable de coeficientes de trayectoria fue encontrado al estimar los modelos con muestras en diferentes periodos de tiempo. (2) Conceptualizar el valor de las patentes en un valor potencial y uno reconocido. También proveer evidencia acerca de que el valor potencial es pequeño al compararlo con el valor que las patentes adquieren con posterioridad. (3) Evidencia acerca de la importancia de considerar la naturaleza longitudinal de los indicatores en el problema de valorización de patentes, especialmente de las citas recibidas, el indicador de valor más utilizado. (4) Introducir una perspectiva multidimensional en el problema de valoración de patentes. Este nuevo enfoque puede ofrecer un entendimiento robusto de las diferentes variables que determinar el valor de las patentes. Contribuciones en el área del PLS PLS Path Modelling comprenden: (5) Evidencia empírica acerca del desempeño de PLS Path Modelling con Modo C. Apropiadamente implemetado, el procedimiento puede adecuadamente capturar algunas de las complejas relaciones dinámicas en los modelos. Nuestra investigación muestra que PLS Path Modelling con Modo C se comporta de acuerdo al marco teórico establecido para los procedimientos PLS y los modelos PLS (Wold, 1982; Krämer, 2006; Hanafi, 2007; Dijkstra, 2010). Es decir, (a) las estimaciones PLS estan siempre sesgadas, (b) las relaciones internas son subestimadas, (c) las relaciones externas son sobrestimadas, (d) el Modo A carece de la propiedad de convergencia monótona, (3) el Modo B tiene la propiedad de convergencia monótona. (6) Evidencia empírica acerca de la convergencia “at large” de PLS Path Modelling con Modo A. (7) Evidencia empírica para los modelos formativos con pocos indicadores (8) Evidencia empírica del desempeño del procedimiento Two-Step PLS Path Modelling con Modo C para estimar efectos no lineales y de interacción entre constructos formativos.

Partial Least Squares (PLS) is an important statistical technique with multipleand diverse applications, used as an effective regression method for correlated orcollinear datasets or for datasets that are not full rank for other reasons. A shorthistory of PLS is followed by a review of the publications where the issues with theapplication PLS that have been discussed. The theoretical basis of PLS is developedfrom the single value decomposition of the covariance, so that the strong links between principal components analysis and within the various PLS algorithms appear as a natural consequence. Latent variable selection by crossvalidation, permutation and information criteriaare examined. A method for plotting crossvalidation results is proposed that makeslatent variable selection less ambiguous than conventional plots. Novel and practicalmethods are proposed to extend published methods for latent variable selection byboth permutation and information criteria from univariate PLS1 models to PLS2 multivariate cases. The numerical method proposed for information criteria is also more general than the algebraic methods for PLS1 that have been recently published as it does not assume any particular form for the PLS regression coefficients. All of these methods have been critically assessed using a number of datasets, selected specifically to represent a diverse set of dimensions and covariance structures. Methods for simulating multivariate datasets were developed that allow controlof correlation and collinearity in both regressors and responses independently. Thisdevelopment also allows control over the variate distributions. Statistical design ofexperiments was used to generate plans for the simulation that allowed the factorsthat infuence PLS model fit and latent variable selection. It was found that all thelatent variable selection methods in the simulation tend to overfit and the feature inthe simulation that causes overfitting has been identified.

<p> Functional Data Analysis (FDA) has attracted substantial attention for the last two decades. Within FDA, classifying curves into two or more categories is consistently of interest to scientists, but multi-class prediction within FDA is challenged in that most classification tools have been limited to binary response applications. The functional logistic regression (FLR) model was developed to forecast a binary response variable in the functional case. In this study, a functional nominal multinomial logit regression (F-NM-LR) model was developed that shifts the FLR model into a multiple logit model. However, the model generates inaccurate parameter function estimates due to multicollinearity in the design matrix. A generalized partial least squares (GPLS) approach with cubic B-spline basis expansions was developed to address the multicollinearity and high dimensionality problems that preclude accurate estimates and curve discrimination with the F-NM-LR model. The GPLS method extends partial least squares (PLS) and improves upon current methodology by introducing a component selection criterion that reconstructs the parameter function with fewer predictors. The GPLS regression estimates are derived via Iteratively ReWeighted Partial Least Squares (IRWPLS), defining a set of uncorrelated latent variables to use as predictors for the F-GPLS-NM-LR model. This methodology was compared to the classic alternative estimation method of principal component regression (PCR) in a simulation study. The performance of the proposed methodology was tested via simulations and applications on a spectrometric dataset. The results indicate that the GPLS method performs well in multi-class prediction with respect to the F-NM-LR model. The main difference between the two approaches was that PCR usually requires more components than GPLS to achieve similar accuracy of parameter function estimates of the F-GPLS-NM-LR model. The results of this research imply that the GPLS method is preferable to the F-NM-LR model, and it is a useful contribution to FDA techniques. This method may be particularly appropriate for practical situations where accurate prediction of a response variable with fewer components is a priority.</p><p>

The current generation of structural equation modeling (SEM) is loosely split in two divergent groups - covariance-based and variance-based structural equation modeling. The relative newness of variance-based SEM has limited the development of techniques that extend its applicability to non-metric data. This study focuses upon the extension of general linear model techniques within the variance-based platform of partial least squares structural equation modeling (PLS-SEM). This modeling procedure receives it name through the iterative PLS‑SEM algorithm's estimates of the coefficients for the partial ordinary least squares regression models in both the measurement model and the overall structural model. This research addresses the following research questions: (1) What are the appropriate measures for data segmentation within PLS‑SEM? (2) What are the appropriate steps for the analysis of rank-ordered path coefficients within PLS‑SEM? and (3) What is an appropriate model selection index for PLS‑SEM? The limited type of data to which PLS-SEM is applicable suggests an opportunity to extend the method for use with different data and as a result a broader number of applications. This study develops and tests several methodologies that are prevalent in the general linear model (GLM). The proposed data segmentation approaches posited and tested through post hoc analysis of structural model. Monte Carlo simulation allows demonstrating the improvement of the proposed model fit indices in comparison to the established indices found within the SEM literature. These posited PLS methods, that are logical transfers of GLM methods, are tested using examples. These tests enable demonstrating the methods and recommending reporting requirements.

Human capital is increasingly believed to play an indispensable role in the growth process; however, adequately measuring its stock remains controversial. Because the estimated impact that human capital has on economic growth is sensitive to the measure of human capital, accurate and consistent measures are desirable. While many measures have been developed, most rely on some proxy of educational experience and are thus plagued with limitations. In this study, I adopt a lifetime earnings approach to estimate the monetary value of the human capital stock for New Zealand. I find that the country's working human capital increased by half between 1981 and 2001, mainly due to rising employment level. This stock was well over double that of physical capital. I also model human capital as a latent variable using a Partial Least Squares approach. Exploratory analyses on a number of countries show that age, gender and education combined can capture 65-97 percent of the explained variation in human capital. JEL Classifications: J24, O47.

The ongoing debate on the evaluative role of citation analysis and the theory of citation recognizes that the citation process is complex and that citation counts are affected by certain extra-scientific or external factors. To date, little effort has been made to explore the effects of various external factors; this thesis addresses this lack. In the context of the various perspectives on citations and citation analysis, this study uses journals as the unit of analysis and investigates what, how, and to what extent extra-scientific factors influence the citation impact of journals. An integrated conceptual model of Journal Citation Impact that takes into account current theoretical positions and prior empirical research findings is developed. It addresses the interrelationships between Journal Citation Impact and a range of external factors (Journal Properties, Journal Visibility, Journal Accessibility, Journal Internationality, Journal Selectivity, Journal Promptness, Journal Editorial Prestige, and Perceived Journal Quality). The proposed conceptual model is novel in that it: (1) incorporates nearly all possible external factors that affect Journal Citation Impact; (2) addresses the complex interrelationships between a number of external factors and Journal Citation Impact in one model; (3) regards both Journal Citation Impact and its external factors as theoretical constructs; and (4) identifies the observed variables of the external factors and Journal Citation Impact. However, because of the difficulties in operationalizing all the theoretical constructs, this conceptual model is simplified to an operational model for empirical testing. The operational model includes the construct Journal Citation Impact and four of its external factors, Journal Properties, Journal Accessibility, Journal Internationality, and Perceived Journal Quality. Structural Equation Modeling (SEM) with Partial Least Squares (PLS) is used to test the operational model with empirical data from 41 research journals in clinical neurology. Data are collected from bibliographic database searching, web searching, printed journals, and from a web-based survey that was conducted to obtain information on perceptions of journal quality. Empirical results of the operational model show that Journal Accessibility, Journal Internationality, and Perceived Journal Quality have large, medium, and small effects respectively on Journal Citation Impact, thus indicating that certain extra-scientific factors can influence Journal Citation Impact significantly. The findings suggest that great care should be taken in interpreting and evaluating the results obtained from citation analysis. In terms of Journal Citation Impact, this research also suggests that various journal citation indicators should be ii used to reflect different aspects of citation impact. By exploring the phenomenological domain in the citing process, this exploratory study not only provides a better understanding of citation analysis, it also contributes to the development of the theory of citation. From the methodological perspective, introducing SEM with PLS to Informetrics and Scientometrics also contributes to the knowledge base of these fields. Pragmatically, the research findings will enhance the judgment of researchers and practitioners such as editors, publishers, librarians and other information specialists in assessing journal performance. Finally, the worldwide survey findings on peer assessment of journal outlets in clinical neurology will be useful for researchers, academics or clinicians in this field.

As a solution to mid-air haptic actuation with strong and continuous tactile force, Magnetic Rendering is presented as an intuitive haptic display method applying an electromagnet array to produce a magnetic field in mid-air where the force field can be felt as magnetic repulsive force exerted on the hand through the attached magnet discs. The magnetic field is generated by a specifically designed electromagnet array driven by direct current. By attaching small magnet discs on the hand, the tactile sensation can be perceived by the user. This method can provide a strong tactile force on multiple points covering user’s hand and avoid cumbersome attachments with wires, thus it is suitable for a co-located visual and haptic display. In my work, the detailed design of the electromagnet array for haptic rendering purposes is introduced, which is modelled and tested using Finite Element Method simulations. The model is characterized mathematically, and three methods for controlling the magnetic field are applied accordingly: direct control, system identification and adaptive control. The performance of the simulated model is evaluated in terms of magnetic field distribution, force strength, operation distance and force stiffness. The control algorithms are implemented and tested on a 3-by-3 and a 15-by-15 model, respectively. Simulations are performed on a 15-by-15 model to generate a haptic human face, which results in a smooth force field and accurate force exertion on the control points.

Despite considerable advances in missing data imputation methods over the last three decades, the problem of missing data remains largely unsolved. Many techniques have emerged in the literature as candidate solutions. These techniques can be categorised into two classes: statistical methods of data imputation and computational intelligence methods of data imputation. Due to the longstanding use of statistical methods in handling missing data problems, it takes quite some time for computational intelligence methods to gain profound attention even though these methods have analogous accuracy, in comparison to other approaches. The merits of both these classes have been discussed at length in the literature, but only limited studies make significant comparison to these classes. This thesis contributes to knowledge by firstly, conducting a comprehensive comparison of standard statistical methods of data imputation, namely, mean substitution (MS), regression imputation (RI), expectation maximization (EM), tree imputation (TI) and multiple imputation (MI) on missing completely at random (MCAR) data sets. Secondly, this study also compares the efficacy of these methods with a computational intelligence method of data imputation, ii namely, a neural network (NN) on missing not at random (MNAR) data sets. The significance difference in performance of the methods is presented. Thirdly, a novel procedure for handling missing data is presented. A hybrid combination of each of these statistical methods with a NN, known here as the post-processing procedure, was adopted to approximate MNAR data sets. Simulation studies for each of these imputation approaches have been conducted to assess the impact of missing values on partial least squares structural equation modelling (PLS-SEM) based on the estimated accuracy of both structural and measurement parameters. The best method to deal with particular missing data mechanisms is highly recognized. Several significant insights were deduced from the simulation results. It was figured that for the problem of MCAR by using statistical methods of data imputation, MI performs better than the other methods for all percentages of missing data. Another unique contribution is found when comparing the results before and after the NN post-processing procedure. This improvement in accuracy may be resulted from the neural network's ability to derive meaning from the imputed data set found by the statistical methods. Based on these results, the NN post-processing procedure is capable to assist MS in producing significant improvement in accuracy of the approximated values. This is a promising result, as MS is the weakest method in this study. This evidence is also informative as MS is often used as the default method available to users of PLS-SEM software.