Relevant bibliographies by topics / Ridge regression estimators

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Ridge regression estimators'

Author: Grafiati
Published: 4 June 2021
Last updated: 7 February 2022

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Journal articles on the topic "Ridge regression estimators"

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Khalaf, G., Kristofer Månsson, and Ghazi Shukur. "Modified Ridge Regression Estimators." Communications in Statistics - Theory and Methods 42, no. 8 (April 15, 2013): 1476–87. http://dx.doi.org/10.1080/03610926.2011.593285.

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Yasin, Seyab, Sultan Salem, Hamdi Ayed, Shahid Kamal, Muhammad Suhail, and Yousaf Ali Khan. "Modified Robust Ridge M-Estimators in Two-Parameter Ridge Regression Model." Mathematical Problems in Engineering 2021 (September 22, 2021): 1–24. http://dx.doi.org/10.1155/2021/1845914.

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The methods of two-parameter ridge and ordinary ridge regression are very sensitive to the presence of the joint problem of multicollinearity and outliers in the y-direction. To overcome this problem, modified robust ridge M-estimators are proposed. The new estimators are then compared with the existing ones by means of extensive Monte Carlo simulations. According to mean squared error (MSE) criterion, the new estimators outperform the least square estimator, ridge regression estimator, and two-parameter ridge estimator in many considered scenarios. Two numerical examples are also presented to illustrate the simulation results.
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Cessie, S. Le, and J. C. Van Houwelingen. "Ridge Estimators in Logistic Regression." Applied Statistics 41, no. 1 (1992): 191. http://dx.doi.org/10.2307/2347628.

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Zinodiny, S. "Bayes minimax ridge regression estimators." Communications in Statistics - Theory and Methods 47, no. 22 (March 7, 2018): 5519–33. http://dx.doi.org/10.1080/03610926.2017.1397167.

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Wu, Jibo, and Chaolin Liu. "Performance of Some Stochastic Restricted Ridge Estimator in Linear Regression Model." Journal of Applied Mathematics 2014 (2014): 1–7. http://dx.doi.org/10.1155/2014/508793.

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This paper considers several estimators for estimating the stochastic restricted ridge regression estimators. A simulation study has been conducted to compare the performance of the estimators. The result from the simulation study shows that stochastic restricted ridge regression estimators outperform mixed estimator. A numerical example has been also given to illustrate the performance of the estimators.
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DEVITA, HANY, I. KOMANG GDE SUKARSA, and I. PUTU EKA N. KENCANA. "KINERJA JACKKNIFE RIDGE REGRESSION DALAM MENGATASI MULTIKOLINEARITAS." E-Jurnal Matematika 3, no. 4 (November 28, 2014): 146. http://dx.doi.org/10.24843/mtk.2014.v03.i04.p077.

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Ordinary least square is a parameter estimations for minimizing residual sum of squares. If the multicollinearity was found in the data, unbias estimator with minimum variance could not be reached. Multicollinearity is a linear correlation between independent variabels in model. Jackknife Ridge Regression(JRR) as an extension of Generalized Ridge Regression (GRR) for solving multicollinearity. Generalized Ridge Regression is used to overcome the bias of estimators caused of presents multicollinearity by adding different bias parameter for each independent variabel in least square equation after transforming the data into an orthoghonal form. Beside that, JRR can reduce the bias of the ridge estimator. The result showed that JRR model out performs GRR model.
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Lukman, Adewale F., B. M. Golam Kibria, Kayode Ayinde, and Segun L. Jegede. "Modified One-Parameter Liu Estimator for the Linear Regression Model." Modelling and Simulation in Engineering 2020 (August 19, 2020): 1–17. http://dx.doi.org/10.1155/2020/9574304.

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Motivated by the ridge regression (Hoerl and Kennard, 1970) and Liu (1993) estimators, this paper proposes a modified Liu estimator to solve the multicollinearity problem for the linear regression model. This modification places this estimator in the class of the ridge and Liu estimators with a single biasing parameter. Theoretical comparisons, real-life application, and simulation results show that it consistently dominates the usual Liu estimator. Under some conditions, it performs better than the ridge regression estimators in the smaller MSE sense. Two real-life data are analyzed to illustrate the findings of the paper and the performances of the estimators assessed by MSE and the mean squared prediction error. The application result agrees with the theoretical and simulation results.
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Arashi, M., S. M. M. Tabatabaey, and M. Hassanzadeh Bashtian. "Shrinkage Ridge Estimators in Linear Regression." Communications in Statistics - Simulation and Computation 43, no. 4 (October 11, 2013): 871–904. http://dx.doi.org/10.1080/03610918.2012.718838.

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Xu, Jianwen, and Hu Yang. "Preliminary test almost unbiased ridge estimator in a linear regression model with multivariate Student-t errors." Acta et Commentationes Universitatis Tartuensis de Mathematica 15, no. 1 (December 11, 2020): 27–43. http://dx.doi.org/10.12697/acutm.2011.15.03.

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In this paper, the preliminary test almost unbiased ridge estimators of the regression coefficients based on the conflicting Wald (W), Likelihood ratio (LR) and Lagrangian multiplier (LM) tests in a multiple regression model with multivariate Student-t errors are introduced when it is suspected that the regression coefficients may be restricted to a subspace. The bias and quadratic risks of the proposed estimators are derived and compared. Sufficient conditions on the departure parameter ∆ and the ridge parameter k are derived for the proposed estimators to be superior to the almost unbiased ridge estimator, restricted almost unbiased ridge estimator and preliminary test estimator. Furthermore, some graphical results are provided to illustrate theoretical results.
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Bhat, S. S., and R. Vidya. "Performance of Ridge Estimators Based on Weighted Geometric Mean and Harmonic Mean." Journal of Scientific Research 12, no. 1 (January 1, 2020): 1–13. http://dx.doi.org/10.3329/jsr.v12i1.40525.

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Ordinary least squares estimator (OLS) becomes unstable if there is a linear dependence between any two predictors. When such situation arises ridge estimator will yield more stable estimates to the regression coefficients than OLS estimator. Here we suggest two modified ridge estimators based on weights, where weights being the first two largest eigen values. We compare their MSE with some of the existing ridge estimators which are defined in the literature. Performance of the suggested estimators is evaluated empirically for a wide range of degree of multicollinearity. Simulation study indicates that the performance of the suggested estimators is slightly better and more stable with respect to degree of multicollinearity, sample size, and error variance.
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Dissertations / Theses on the topic "Ridge regression estimators"

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Williams, Ulyana P. "On Some Ridge Regression Estimators for Logistic Regression Models." FIU Digital Commons, 2018. https://digitalcommons.fiu.edu/etd/3667.

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The purpose of this research is to investigate the performance of some ridge regression estimators for the logistic regression model in the presence of moderate to high correlation among the explanatory variables. As a performance criterion, we use the mean square error (MSE), the mean absolute percentage error (MAPE), the magnitude of bias, and the percentage of times the ridge regression estimator produces a higher MSE than the maximum likelihood estimator. A Monto Carlo simulation study has been executed to compare the performance of the ridge regression estimators under different experimental conditions. The degree of correlation, sample size, number of independent variables, and log odds ratio has been varied in the design of experiment. Simulation results show that under certain conditions, the ridge regression estimators outperform the maximum likelihood estimator. Moreover, an empirical data analysis supports the main findings of this study. This thesis proposed and recommended some good ridge regression estimators of the logistic regression model for the practitioners in the field of health, physical and social sciences.
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Zaldivar, Cynthia. "On the Performance of some Poisson Ridge Regression Estimators." FIU Digital Commons, 2018. https://digitalcommons.fiu.edu/etd/3669.

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Multiple regression models play an important role in analyzing and making predictions about data. Prediction accuracy becomes lower when two or more explanatory variables in the model are highly correlated. One solution is to use ridge regression. The purpose of this thesis is to study the performance of available ridge regression estimators for Poisson regression models in the presence of moderately to highly correlated variables. As performance criteria, we use mean square error (MSE), mean absolute percentage error (MAPE), and percentage of times the maximum likelihood (ML) estimator produces a higher MSE than the ridge regression estimator. A Monte Carlo simulation study was conducted to compare performance of the estimators under three experimental conditions: correlation, sample size, and intercept. It is evident from simulation results that all ridge estimators performed better than the ML estimator. We proposed new estimators based on the results, which performed very well compared to the original estimators. Finally, the estimators are illustrated using data on recreational habits.
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Gripencrantz, Sarah. "Evaluating the Use of Ridge Regression and Principal Components in Propensity Score Estimators under Multicollinearity." Thesis, Uppsala universitet, Statistiska institutionen, 2014. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-226924.

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Multicollinearity can be present in the propensity score model when estimating average treatment effects (ATEs). In this thesis, logistic ridge regression (LRR) and principal components logistic regression (PCLR) are evaluated as an alternative to ML estimation of the propensity score model. ATE estimators based on weighting (IPW), matching and stratification are assessed in a Monte Carlo simulation study to evaluate LRR and PCLR. Further, an empirical example of using LRR and PCLR on real data under multicollinearity is provided. Results from the simulation study reveal that under multicollinearity and in small samples, the use of LRR reduces bias in the matching estimator, compared to ML. In large samples PCLR yields lowest bias, and typically was found to have the lowest MSE in all estimators. PCLR matched ML in bias under IPW estimation and in some cases had lower bias. The stratification estimator was heavily biased compared to matching and IPW but both bias and MSE improved as PCLR was applied, and for some cases under LRR. The specification with PCLR in the empirical example was usually most sensitive as a strongly correlated covariate was included in the propensity score model.
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Shah, Smit. "Comparison of Some Improved Estimators for Linear Regression Model under Different Conditions." FIU Digital Commons, 2015. http://digitalcommons.fiu.edu/etd/1853.

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Multiple linear regression model plays a key role in statistical inference and it has extensive applications in business, environmental, physical and social sciences. Multicollinearity has been a considerable problem in multiple regression analysis. When the regressor variables are multicollinear, it becomes difficult to make precise statistical inferences about the regression coefficients. There are some statistical methods that can be used, which are discussed in this thesis are ridge regression, Liu, two parameter biased and LASSO estimators. Firstly, an analytical comparison on the basis of risk was made among ridge, Liu and LASSO estimators under orthonormal regression model. I found that LASSO dominates least squares, ridge and Liu estimators over a significant portion of the parameter space for large dimension. Secondly, a simulation study was conducted to compare performance of ridge, Liu and two parameter biased estimator by their mean squared error criterion. I found that two parameter biased estimator performs better than its corresponding ridge regression estimator. Overall, Liu estimator performs better than both ridge and two parameter biased estimator.
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Binard, Carole. "Estimation de fonctions de régression : sélection d'estimateurs ridge, étude de la procédure PLS1 et applications à la modélisation de la signature génique du cancer du poumon." Thesis, Nice, 2016. http://www.theses.fr/2016NICE4015.

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Cette thèse porte sur l’estimation d'une fonction de régression fournissant la meilleure relation entredes variables pour lesquelles on possède un certain nombre d’observations. Une première partie portesur une étude par simulation de deux méthodes automatiques de sélection du paramètre de laprocédure d'estimation ridge. D'un point de vue plus théorique, on présente et compare ensuite deuxméthodes de sélection d'un multiparamètre intervenant dans une procédure d'estimation d'unefonction de régression sur l'intervalle [0,1]. Dans une deuxième partie, on étudie la qualité del'estimateur PLS1, d'un point de vue théorique, à travers son risque quadratique et, plus précisément,le terme de variance dans la décomposition biais/variance de ce risque. Enfin, dans une troisièmepartie, une étude statistique sur données réelles est menée afin de mieux comprendre la signaturegénique de cellules cancéreuses à partir de la signature génique des sous-types cellulaires constituantle stroma tumoral associé
This thesis deals with the estimation of a regression function providing the best relationship betweenvariables for which we have some observations. In a first part, we complete a simulation study fortwo automatic selection methods of the ridge parameter. From a more theoretical point of view, wethen present and compare two selection methods of a multiparameter, that is used in an estimationprocedure of a regression function on [0,1]. In a second part, we study the quality of the PLS1estimator through its quadratic risk and, more precisely, the variance term in its bias/variancedecomposition. In a third part, a statistical study is carried out in order to explain the geneticsignature of cancer cells thanks to the genetic signatures of cellular subtypes which compose theassociated tumor stroma
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Wissel, Julia. "A new biased estimator for multivariate regression models with highly collinear variables." Doctoral thesis, kostenfrei, 2009. http://www.opus-bayern.de/uni-wuerzburg/volltexte/2009/3638/.

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Nakamura, Karina Gernhardt. "Multicolinearidade em modelos de regressão logística." Universidade de São Paulo, 2013. http://www.teses.usp.br/teses/disponiveis/45/45133/tde-28052013-222241/.

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Neste trabalho estudamos os efeitos da multicolinearidade em modelos de regressão logística e apresentamos estimadores viesados para que tais efeitos fossem minimizados. Primeiramente, o modelo de regressão logística e o processo para a estimação dos parâmetros foram apresentados. Foram feitos, também, alguns testes para avaliar a significância dos mesmos, bem como técnicas para analisar a qualidade do ajuste do modelo. Em seguida, os efeitos da multicolinearidade na estimação dos parâmetros e na sua inferência foram avaliados, bem como técnicas para o seu diagnóstico. Para amenizar o efeito deste problema, apresentamos dois estimadores alternativos ao de máxima verossimilhança: estimador em cristas e estimador em componentes principais. Comparamos, então, o desempenho dos três estimadores na forma de um estudo de simulação e de uma aplicação em um conjunto de dados reais. O principal resultado obtido foi que, na presença de multicolinearidade, os estimadores alternativos conseguiram um melhor ajuste em comparação ao de máxima verossimilhança, além de minimizar os seus efeitos.
This work proposes the use of some biased estimators to investigate whether is possible minimize the multicollinearity effects in logistic regression models. Initially, the latter model was presented, as well as its fitting process (therefore obtaining the maximum likelihood estimator), some tests to evaluate the significance of the parameters and techniques to analyze goodness of fit were also considered. Furthermore, the effects of multicollinearity in the fitting process and in the parameters inference were discussed, as well as techniques to identify the presence of multicollinearity. In order to diminish the effect of this problem, two alternative estimators were presented: ridge estimator and principal component estimator. Therefore, these three estimators performances were compared using a simulation study and applied in a real data set. The manly conclusion was that, in the presence of multicollinearity, the alternative estimators performed better than the maximum likelihood estimator, besides reducing its effects.
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Shehzad, Muhammad Ahmed. "Pénalisation et réduction de la dimension des variables auxiliaires en théorie des sondages." Phd thesis, Université de Bourgogne, 2012. http://tel.archives-ouvertes.fr/tel-00812880.

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Les enquêtes par sondage sont utiles pour estimer des caractéristiques d'une populationtelles que le total ou la moyenne. Cette thèse s'intéresse à l'étude detechniques permettant de prendre en compte un grand nombre de variables auxiliairespour l'estimation d'un total.Le premier chapitre rappelle quelques définitions et propriétés utiles pour lasuite du manuscrit : l'estimateur de Horvitz-Thompson, qui est présenté commeun estimateur n'utilisant pas l'information auxiliaire ainsi que les techniques decalage qui permettent de modifier les poids de sondage de facon à prendre encompte l'information auxiliaire en restituant exactement dans l'échantillon leurstotaux sur la population.Le deuxième chapitre, qui est une partie d'un article de synthèse accepté pourpublication, présente les méthodes de régression ridge comme un remède possibleau problème de colinéarité des variables auxiliaires, et donc de mauvais conditionnement.Nous étudions les points de vue "model-based" et "model-assisted" dela ridge regression. Cette technique qui fournit de meilleurs résultats en termed'erreur quadratique en comparaison avec les moindres carrés ordinaires peutégalement s'interpréter comme un calage pénalisé. Des simulations permettentd'illustrer l'intérêt de cette technique par compar[a]ison avec l'estimateur de Horvitz-Thompson.Le chapitre trois présente une autre manière de traiter les problèmes de colinéaritévia une réduction de la dimension basée sur les composantes principales. Nousétudions la régression sur composantes principales dans le contexte des sondages.Nous explorons également le calage sur les moments d'ordre deux des composantesprincipales ainsi que le calage partiel et le calage sur les composantes principalesestimées. Une illustration sur des données de l'entreprise Médiamétrie permet deconfirmer l'intérêt des ces techniques basées sur la réduction de la dimension pourl'estimation d'un total en présence d'un grand nombre de variables auxiliaires
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-Shuenn, Deng Wen, and 鄧文舜. "The Study of Kernel Regression Function Polygons and Local Linear Ridge Regression Estimators." Thesis, 2002. http://ndltd.ncl.edu.tw/handle/60535152004594408945.

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博士
國立東華大學
應用數學系
90
In the field of random design nonparametric regression, we examine two kernel estimators involving, respectively, piecewise linear interpolation of kernel regression function estimates and local ridge regression. Efforts dedicated to understanding their properties bring forth the following main messages. The kernel estimate of a regression function inherits its smoothness properties from the kernel function chosen by the investigator. Nevertheless, practical regression function estimates are often presented in interpolated form, using the exact kernel estimates only at some equally spaced grids of points. The asymptotic integrated mean square error (AIMSE) properties of such polygon type estimate, namely kernel regression function polygons (KRFP), are investigated. Call the "optimal kernel" the minimizer of the AIMSE. Epanechnikov kernel is not the optimal kernel unless for the case that the distance between every two consecutive grids is of smaller order in magnitude than the bandwidth used by the kernel regression function estimator. If the distance and bandwidth are of the same order in magnitude, we obtain the optimal kernel from the class of degree-two polynomials through numerical calculations. In this case, the best AIMSE performances deteriorate as the distance is increased to reduce the computational effort. When the distance is of larger order in magnitude than the bandwidth, then uniform kernel serves as the optimal kernel for KRFP. Local linear estimator (LLE) has many attractive asymptotic features. In finite sample situations, however, its conditional variance may become arbitrarily large. To cope with this difficulty, which can translate into the spurious rough appearance of the regression function estimate when design becomes sparse or clustered, Seifert and Gasser (1996)suggest "ridging" the LLE and propose the local linear ridge regression estimator (LLRRE). In this dissertation, local and numerical properties of the LLRRE are studied. It is shown that its finite sample mean square errors, both conditional and unconditional, are bounded above by finite constants. If the ridge regression parameters are not selected properly, then the resulting LLRRE suffers some drawbacks. For example, it is asymptotically biased and has boundary effects, and fails to inherit the nice asymptotic bias quality of the LLE. Letting the ridge parameters depend on sample size and converge to 0 as the sample size increases, we are able to ensure LLRRE the nice asymptotic features of the LLE under some mild conditions. Simulation studies demonstrate that the LLRRE using cross-validated bandwidth and ridge parameters could have smaller sample mean integrated square error than the LLE using cross-validated bandwidth, in reasonable sample sizes.
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Chen, Ai-Chun, and 陳愛群. "A class of Liu-type estimators based on ridge regression under multicollinearity with an application to mixture experiments." Thesis, 2015. http://ndltd.ncl.edu.tw/handle/bquhze.

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碩士
國立中央大學
統計研究所
103
In the linear regression, the least square estimator does not perform well in terms of mean squared error when multicollinearity exists. The problem of multicollinearity occurs in industrial mixture experiments, where regressors are constrained.Hoerl and Kennard (1970) proposed the ordinary ridge estimator to overcome the problem of the least squared estimator under multicollinearity. Recently, the ridge regression is successfully applied to mixture experiments. However, the application of ridge becomes difficult if the linear model has the intercept term and the regressors are standardized as occurring in mixture experiments. This paper considers a special class of Liu-type estimators (Liu, 2003) with intercept. We derive the theoretical formula of the mean squared error for the proposed method. We perform simulations to compare the proposed estimator with the ridge estimator in terms of mean squared error. We demonstrate this special class using the dataset on Portland cement with mixture experiment (Woods et al., 1932).
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Books on the topic "Ridge regression estimators"

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Gruber, Marvin H. J. Regression estimators: A comparative study. 2nd ed. Baltimore: Johns Hopkins University Press, 2010.

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Gruber, Marvin H. J. Regression estimators: A comparative study. Boston: Academic Press, 1990.

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Gruber, Marvin H. J. Regression estimators: A comparative study. Boston: Academic Press, 1992.

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Regression estimators: A comparative study. 2nd ed. Baltimore: Johns Hopkins University Press, 2010.

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Gruber, Marvin H. J. Regression estimators: A comparative study. 2nd ed. Baltimore: Johns Hopkins University Press, 2010.

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Improving efficiency by shrinkage: The James-Stein and ridge regression estimators. New York: Marcel Dekker, 1998.

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Ahmed, S. E. (Syed Ejaz), 1957- editor of compilation, ed. Perspectives on big data analysis: Methodologies and applications : International Workshop on Perspectives on High-Dimensional Data Anlaysis II, May 30-June 1, 2012, Centre de Recherches Mathématiques, University de Montréal, Montréal, Québec, Canada. Providence, Rhode Island: American Mathematical Society, 2014.

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Book chapters on the topic "Ridge regression estimators"

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Yüzbaşı, Bahadır, and S. Ejaz Ahmed. "Shrinkage Ridge Regression Estimators in High-Dimensional Linear Models." In Advances in Intelligent Systems and Computing, 793–807. Berlin, Heidelberg: Springer Berlin Heidelberg, 2015. http://dx.doi.org/10.1007/978-3-662-47241-5_67.

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Akdeniz, Esra, and Fikri Akdeniz. "The Lawless-Wang's Operational Ridge Regression Estimator under the LINEX Loss Function." In Statistics: A Series of Textbooks and Monographs, 201–13. Chapman and Hall/CRC, 2005. http://dx.doi.org/10.1201/9781420028690.ch13.

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Conference papers on the topic "Ridge regression estimators"

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Suhail, Muhammad, and Sohail Chand. "Performance of some new ridge regression estimators." In 2019 13th International Conference on Mathematics, Actuarial Science, Computer Science and Statistics (MACS). IEEE, 2019. http://dx.doi.org/10.1109/macs48846.2019.9024784.

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Zahari, Siti Meriam, Norazan Mohamed Ramli, Balkiah Moktar, and Mohammad Said Zainol. "The comparison between several robust ridge regression estimators in the presence of multicollinearity and multiple outliers." In STATISTICS AND OPERATIONAL RESEARCH INTERNATIONAL CONFERENCE (SORIC 2013). AIP Publishing LLC, 2014. http://dx.doi.org/10.1063/1.4894363.

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Liu, Meimei, Jean Honorio, and Guang Cheng. "Statistically and Computationally Efficient Variance Estimator for Kernel Ridge Regression." In 2018 56th Annual Allerton Conference on Communication, Control, and Computing (Allerton). IEEE, 2018. http://dx.doi.org/10.1109/allerton.2018.8635936.

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Chang, Xinfeng. "On the almost unbiased Ridge and Liu estimator in the Logistic regression model." In 2015 International Conference on Social Science, Education Management and Sports Education. Paris, France: Atlantis Press, 2015. http://dx.doi.org/10.2991/ssemse-15.2015.424.

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Ariffin, Syaiba Balqish, and Habshah Midi. "The effect of high leverage points on the logistic ridge regression estimator having multicollinearity." In PROCEEDINGS OF THE 3RD INTERNATIONAL CONFERENCE ON MATHEMATICAL SCIENCES. AIP Publishing LLC, 2014. http://dx.doi.org/10.1063/1.4882622.

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Zhou, Daoqing, and Jibo Wu. "The properties of stochastic restricted two-parameter ridge type estimator in linear regression model." In ICBDC '18: 2018 International Conference on Big Data and Computing. New York, NY, USA: ACM, 2018. http://dx.doi.org/10.1145/3220199.3220213.

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Pati, Kafi Dano, Robiah Adnan, Bello Abdulkadir Rasheed, and Muhammad Alias MD. J. "Estimation parameters using Bisquare weighted robust ridge regression BRLTS estimator in the presence of multicollinearity and outliers." In ADVANCES IN INDUSTRIAL AND APPLIED MATHEMATICS: Proceedings of 23rd Malaysian National Symposium of Mathematical Sciences (SKSM23). Author(s), 2016. http://dx.doi.org/10.1063/1.4954633.

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Nguyen, Thien Duy, John Craig Wells, Paritosh Mokhasi, and Dietmar Rempfer. "POD-Based Estimations of the Flowfield From PIV Wall Gradient Measurements in the Backward-Facing Step Flow." In ASME 2010 3rd Joint US-European Fluids Engineering Summer Meeting collocated with 8th International Conference on Nanochannels, Microchannels, and Minichannels. ASMEDC, 2010. http://dx.doi.org/10.1115/fedsm-icnmm2010-30657.

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In this paper, particle image velocimetry (PIV) results from a backward-facing step flow, of which Reynolds number is 2800 based on free stream velocity and step height (h = 16.5 mm), are used to demonstrate the capability of proper orthogonal decomposition (POD)-based estimation models. Three-component PIV velocity fields are decomposed into a set of spatial basis functions and a set of temporal coefficients. The estimation models are built to relate the low-order POD coefficients, determined from an ensemble of 1050 PIV fields by the “snapshot” method, and the time-resolved wall gradients, measured by a near-wall measurement technique called stereo interfacial PIV. These models are evaluated in terms of reconstruction and prediction of the low-order temporal POD coefficients of the velocity fields. In order to determine the coefficients of the estimation models, linear stochastic estimation (LSE), quadratic stochastic estimation (QSE), principal component regression (PCR) and kernel ridge regression (KRR) are applied. In addition, we introduce a possibility of multi-time POD-based estimations in which past and future information of the wall gradient events is used separately or combined. The results show that the multi-time estimation approaches can improve the prediction process. Among these approaches, the proposed multi-time KRR-POD estimation with optimized time duration of wall gradient information in the past yields the best prediction.
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Shevchenko, Maksim, Sergiy Yepifanov, and Igor Loboda. "Ridge Estimation and Principal Component Analysis to Solve an Ill-Conditioned Problem of Estimating Unmeasured Gas Turbine Parameters." In ASME Turbo Expo 2013: Turbine Technical Conference and Exposition. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/gt2013-94496.

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This paper addresses the problem of estimation of unmeasured gas turbine engine variables using statistical analysis of measured data. Possible changes of an engine health condition and lack of information about these changes caused by limited instrumentation are taken into account. Engine thrust is under consideration as one of the most important unmeasured parameters. Two common methods of aircraft gas turbine engine (GTE) thrust monitoring and their errors due to health condition changes are analyzed. Additionally, two mathematical techniques that allow reducing in-flight thrust estimation errors in the case of GTE deterioration are suggested and verified in the paper. They are a ridge trace and a principal component analysis. A turbofan engine has been chosen as a test case. The engine has five measured variables and 23 health parameters to describe its health condition. Measurement errors are simulated using a generator of random numbers with the normal distribution. The engine is presented in calculations by its nonlinear component level model (CLM). Results of the comparison of thrust estimates computed by the CLM and the proposed techniques confirm accuracy of the techniques. The regression model on principal components has demonstrated the highest accuracy.
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