Dissertations / Theses on the topic 'Best linear unbiased estimator'

Thesis (Ph. D.)--University of New Orleans, 2003.
Title from electronic submission form. "A dissertation ... in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the Department of Electrical Engineering"--Dissertation t.p. Vita. Includes bibliographical references.

Thesis (Ph. D.) -- University of Maryland, College Park, 2007.
Thesis research directed by: Mathematical Statistics Program. Title from t.p. of PDF. Includes bibliographical references. Published by UMI Dissertation Services, Ann Arbor, Mich. Also available in paper.

The main focus of many agricultural, ecological and environmental studies is to develop well designed, cost-effective and efficient sampling designs. Ranked set sampling (RSS) is one of those sampling methods that can help accomplish such objectives by incorporating prior information and expert knowledge to the design. In this thesis, new RSS schemes are suggested for efficiently estimating the population mean. These sampling schemes can be used as cost-effective alternatives to the traditional simple random sampling (SRS) and RSS schemes. It is shown that the mean estimators under the proposed sampling schemes are at least as efficient as the mean estimator with SRS. We consider the best linear unbiased estimators (BLUEs) and the best linear invariant estimators (BLIEs) for the unknown parameters (location and scale) of a location-scale family of distributions under double RSS (DRSS) scheme. The BLUEs and BLIEs with DRSS are more precise than their counterparts based on SRS and RSS schemes. We also consider the BLUEs based on DRSS and ordered DRSS (ODRSS) schemes for the unknown parameters of a simple linear regression model using replicated observations. It turns out that, in terms of relative efficiencies, the BLUEs under ODRSS are better than the BLUEs with SRS, RSS, ordered RSS (ORSS) and DRSS schemes. Quality control charts are widely recognized for their potential to be a powerful process monitoring tool of the statistical process control. These control charts are frequently used in many industrial and service organizations to monitor in-control and out-of-control performances of a production or manufacturing process. The RSS schemes have had considerable attention in the construction of quality control charts. We propose new exponentially weighted moving average (EWMA) control charts for monitoring the process mean and the process dispersion based on the BLUEs obtained under ORSS and ODRSS schemes. We also suggest an improved maximum EWMA control chart for simultaneously monitoring the process mean and dispersion based on the BLUEs with ORSS scheme. The proposed EWMA control charts perform substantially better than their counterparts based on SRS and RSS schemes. Finally, some new EWMA charts are also suggested for monitoring the process dispersion using the best linear unbiased absolute estimators of the scale parameter under SRS and RSS schemes.

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CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior
Este trabalho tem como objetivo o estudo de técnicas para a estimação da amplitude de sinais no calorímetro de telhas (TileCal) do ATLAS no LHC em cenários de alta luminosidade. Em alta luminosidade, sinais provenientes de colisões adjacentes são observados, ocasionando o efeito de empilhamento de sinais. Neste ambiente, o método COF (do inglês, Constrained Optimal Filter), apresenta desempenho superior ao algoritmo atualmente implementado no sistema. Entretanto, o COF requer a inversão de matrizes para o cálculo da pseudo-inversa de uma matriz de convolução, dificultando sua implementação online. Para evitar a inversão de matrizes, este trabalho apresenta métodos interativos, para a daptação do COF, que resultam em operações matemáticas simples. Baseados no Gradiente Descendente, os resultados demonstraram que os algoritmos são capazes de estimar a amplitude de sinais empilhados, além do sinal de interesse com eficiência similar ao COF. Visando a implementação online, este trabalho apresenta estudos sobre a complexidade dos métodos iterativos e propõe uma arquitetura de processamento em FPGA. Baseado em uma estrutura sequencial e utilizando lógica aritmética em ponto fixo, os resultados demonstraram que a arquitetura desenvolvida é capaz executar o método iterativo, atendendo os requisitos de tempo de processamento exigidos no TileCal.
This work aims at the study of techniques for online energy estimation in the ATLAS hadronic Calorimeter (TileCal) on the LHC collider. During further periods of the LHC operation, signals coming from adjacent collisions will be observed within the same window, producing a signal superposition. In this environment, the energy reconstruction method COF (Constrained Optimal Filter) outperforms the algorithm currently implemented in the system. However , the COF method requires an inversion of matrices and its online implementation is not feasible. To avoid such inversion of matrices, this work presents iteractive methods to implement the COF, resulting in simple mathematical operations. Based on the Gradient Descent, the results demonstrate that the algorithms are capable of estimating the amplitude of the superimposed signals with efficiency similar to COF. In addition, a processing architecture for FPGA implementation is proposed. The analysis has shown that the algorithms can be implemented in the new TilaCal electronics, reaching the processing time requirements.

This dissertation consists of two parts. The first part deals with the performance appraisal of estimation algorithms. The second part focuses on the application of estimation algorithms to target tracking. Performance appraisal is crucial for understanding, developing and comparing various estimation algorithms. In particular, with the evolvement of estimation theory and the increase of problem complexity, performance appraisal is getting more and more challenging for engineers to make comprehensive conclusions. However, the existing theoretical results are inadequate for practical reference. The first part of this dissertation is dedicated to performance measures which include local performance measures, global performance measures and model distortion measure. The second part focuses on application of the recursive best linear unbiased estimation (BLUE) or lineae minimum mean square error (LMMSE) estimation to nonlinear measurement problem in target tracking. Kalman filter has been the dominant basis for dynamic state filtering for several decades. Beyond Kalman filter, a more fundamental basis for the recursive best linear unbiased filtering has been thoroughly investigated in a series of papers by Dr. X. Rong Li. Based on the so-called quasirecursive best linear unbiased filtering technique, the constraints of the Kalman filter Linear-Gaussian assumptions can be relaxed such that a general linear filtering technique for nonlinear systems can be achieved. An approximate optimal BLUE filter is implemented for nonlinear measurements in target tracking which outperforms the existing method significantly in terms of accuracy, credibility and robustness.

In most breeding programmes breeders use phenotypic data obtained in breeding trials to rank the performance of the parents or progeny on pre-selected performance criteria. Through this ranking the best candidates are identified and selected for breeding or production purposes. Best Linear Unbiased Prediction (BLUP), is an efficient selection method to use, combining information into a single index. Unbalanced or messy data is frequently found in tree breeding trial data. Trial individuals are related and a degree of correlation is expected between individuals over sites, which can lead to collinearity in the data which may lead to instability in certain selection models. A high degree of collinearity may cause problems and adversely affect the prediction of the breeding values in a BLUP selection index. Simulation studies have highlighted that instability is a concern and needs to be investigated in experimental data. The occurrence of instability, relating to collinearity, in BLUP of tree breeding data and possible methods to deal with it were investigated in this study. Case study data from 39 forestry breeding trials (three generations) of Eucalyptus grandis and 20 trials of Pinus patula (two generations) were used. A series of BLUP predictions (rankings) using three selection traits and 10 economic weighting sets were made. Backward and forward prediction models with three different matrix inversion techniques (singular value decomposition, Gaussian elimination - partial and full pivoting) and an adapted ridge regression technique were used in calculating BLUP indices. A Delphi and Clipper version of the same BLUP programme which run with different computational numerical precision were used and compared. Predicted breeding values (forward prediction) were determined in the F1 and F2 E. grandis trials and F1 P. patula trials and realised breeding performance (backward prediction) was determined in the F2 and F3 E. grandis trials and F2 P. patula trials. The accuracy (correlation between the predicted breeding values and realised breeding performance) was estimated in order to assess the efficiency of the predictions and evaluate the different matrix inversion methods. The magnitude of the accuracy (correlations) was found to mostly be of acceptable magnitude when compared to the heritability of the compound weighted trait in the F1F2 E. grandis scenarios. Realised genetic gains were also calculated for each method used. Instability was observed in both E. grandis and P. patula breeding data in the study, and this may cause a significant loss in realised genetic gains. Instability can be identified by examining the matrix calculated from the product of the phenotypic covariance matrix with its inverse, for deviations from the expected identity pattern. Results of this study indicate that it may not always be optimal to use a higher numerical precision programme when there is collinearity in the data and instability in the matrix calculations. In some cases, where there is a large amount of collinearity, the use of a higher precision programme for BLUP calculations can significantly increase or decrease the accuracy of the rankings. The different matrix inversion techniques particularly SVD and adapted ridge regression did not perform much better than the full pivoting technique. The study found that it is beneficial to use the full pivoting Gaussian elimination matrix inversion technique in preference to the partial pivoting Gaussian elimination matrix inversion technique for both high and lower numerical precision programmes.
Thesis (PhD)--University of Pretoria, 2013.
gm2014
Genetics
unrestricted

Advances in molecular marker technologies have led to the development of high throughput genotyping techniques such as Genotyping by Sequencing (GBS), driving the application of genomics in crop research and breeding. They have also supported the use of novel mapping approaches, including Multi-parent Advanced Generation Inter-Cross (MAGIC) populations which have increased precision in identifying markers to inform plant breeding practices. In the first part of this thesis, a high density physical map derived from GBS was used to identify QTLs controlling key agronomic traits of wheat in a genome-wide association study (GWAS) and to demonstrate the practicability of genomic selection for predicting the trait values. The results from GBS were compared to a previous study conducted on the same association mapping panel using a less dense physical map derived from diversity arrays technology (DArT) markers. GBS detected more QTLs than DArT markers although some of the QTLs were detected by DArT markers alone. Prediction accuracies from the two marker platforms were mostly similar and largely dependent on trait genetic architecture. The second part of this thesis focused on MAGIC populations, which incorporate diversity and novel allelic combinations from several generations of recombination. Pedigrees representing a wild rice MAGIC population were used to model MAGIC populations by simulation to assess the level of recombination and creation of novel haplotypes. The wild rice species are an important reservoir of beneficial genes that have been variously introgressed into rice varieties using bi-parental population approaches. The level of recombination was found to be highly dependent on the number of crosses made and on the resulting population size. Creation of MAGIC populations require adequate planning in order to make sufficient number of crosses that capture optimal haplotype diversity. The third part of the thesis considers models that have been proposed for genomic prediction. The ridge regression best linear unbiased prediction (RR-BLUP) is based on the assumption that all genotyped molecular markers make equal contributions to the variations of a phenotype. Information from underlying candidate molecular markers are however of greater significance and can be used to improve the accuracy of prediction. Here, an existing Differentially Penalized Regression (DiPR) model which uses modifications to a standard RR-BLUP package and allows two or more marker sets from different platforms to be independently weighted was used. The DiPR model performed better than single or combined marker sets for predicting most of the traits both in a MAGIC population and an association mapping panel. Overall the work presented in this thesis shows that while these techniques have great promise, they should be carefully evaluated before introduction into breeding programmes.

The class of models which is studied in this paper, multi-unit longitudinal models, combines both the cross-sectional and the longitudinal aspects of observations. Many empirical investigations involve the analysis of data structures that are both cross-sectional (observations are taken on several units at a specific time period or at a specific location) and longitudinal (observations on the same unit are taken over time or space). Multi-unit longitudinal data structures arise in economics and business where panels of subjects are studied over time, biostatistics where groups of patients on different treatments are observed over time, and in situations where data are taken over time and space. Modelling issues in multi-unit longitudinal models with random coefficients and patterned correlation structure are illustrated in the context of two data sets. The first data set deals with short time series data on annual death rates and alcohol consumption for twenty-five European countries. The second data set deals with glaceologic time series data on snow temperature at 14 different locations within a small glacier in the Austrian Alps. A practical model building approach, consisting of model specification, estimation, and diagnostic checking, is outlined. (author's abstract)
Series: Forschungsberichte / Institut für Statistik

碩士
嶺東科技大學
資訊管理與應用研究所
100
The Global Positioning System (GPS) is a successful and best satellite navigation system that provides mobile location in all environments of outdoor. But it cannot keep the best line of sight, and the accuracy of location will be degraded in the environment of poor satellite signal. Thus, the wireless sensor network is a popular research project in recent years. The location technologies include received signal strength (RSS), time of arrival (TOA), time difference of arrival (TDOA), and angle of arrival (AOA). However, the non-line of sight and the multiple path will effect positioning performance, the positioning algorithm is necessary to reduce the errors and improve the estimation accuracy. However, the received signal strength (RSS) does not require time synchronization. Therefore, we can easy to get the positioning estimation. In establish and development costs, RSS is lower than other positioning methods; and it through the signal strength to transfer the distance, and the location of the target can be obtained. This study is based on RSS positioning technology to discuss the accurate algorithms and signal model by positioning algorithms. This study uses the best linear unbiased estimator (BLUE) for the signal model. By comparing the positioning performance, we use the least square (LS) method, the weighted least squares (WLS) method, and blind minimax estimation (BME) mean-square-error method. Finally, the simulation results show that the performance of blind minimax estimation (BME) mean-square-error method is better than the least square (LS) method and the weighted least squares (WLS) method.

Godambe (1955) give a general finite population sampling model and proved that a best linear unbiased estimator (BLUE) of population total does not exist when there is no measurement error. In this research, Godambe’s linear estimator is expanded to include two types of measurement errors and their mixture. We check Godambe’s non-existence theorem and explore the method to develop the best linear unbiased estimator of the latent population total by using individual unbiased constraints and average unbiased constraints, respectively. We start from Godambe’s general framework and then reduce to two probability models which are less general than Godambe’s. The model is developed under unequal probability sampling without replacement. As a special case, the model under simple random sampling without replacement can be derived directly based on the results. The traditional definition of inclusion probability is extended and applied to the unequal probability sampling. These results connect the traditional sampling method and the design-based method using random permutation models based on the work of Royall (1976) as proposed by Stanek, Singer and Lencina (2004). We also examine the relationship among Godambe’s general finite sampling model, the expanded model finite population model and the finite population mixed model. Also, we are able to give another set of solutions by giving a distribution to the sample latent values. The research can serve as the basis for extensions to multi-stage sampling or other complex sampling designs.

碩士
國立交通大學
統計學系
85
Nonparametric regression problems can be modeled as nonparmetric mixed-effects models. The Gauss-Markov theorems of nonparametric mixed-effects models suggest the best linear unbiased prediction(BLUP) (Huang and Lu,1997). Owing to the spatial adaptivity and multiresolution analysis property, wavelets can be useful basis to represent complicated signal variability. This report will generalize the perspective of BLUP on the wavelet representation. It suggests new shrinkage methods to denoise the observed signals efficiently as demonstrated in this report. Shrinkage parameters are estimated by the data automatically in speed. The resulting adaptive wavelet shrinkage methods can reconstrct signals with small average square errors without increasing the computational cost. These methods also work for arbitary designs, including the fixed dyadic designs.