Date of Award

2013

Degree Type

Dissertation

Degree Name

Ph.D.

Department

Mathematics and Statistics

First Advisor

Syed, Ahmed Ejaz

Second Advisor

Hussein, Abdulkadir A.

Keywords

Applied sciences, Computier vision, Embadded face recognition, Embedded system, Facerecognition, Lbp, Sparse face recognitionestimator, Shrinkge estimator, Spatial regrsion models

Rights

CC BY-NC-ND 4.0

Abstract

In this dissertation, we study the asymptotic properties of pretest and shrinkage estimators of the large-scale effect in some spatial regression models, and compare their relative performance with respect to the classical maximum likelihood estimator (MLE) analytically and numerically through Monte Carlo experiments and real data examples. The shrinkage estimators were also numerically compared with three penalty estimators, namely, the LASSO, adaptive LASSO, and the SCAD penalty functions. A linear model with conditional autoregressive errors was studied in Chapter 2. The asymptotic properties of the shrinkage estimators, under local alternatives, were established, including the derivations of the asymptotic distributional bias, asymptotic mean squared error matrix, and the asymptotic quadratic risk. These results showed the effectiveness of the suggested estimation technique. Monte Carlo experiments with two real data examples were conducted to demonstrate the superiority of the proposed shrinkage estimators over the MLE and the penalty estimators. In Chapter 3, we consider another spatial case of a linear model with simultaneous autoregressive errors. We study the properties of the shrinkage estimators and compare their performance with the penalty estimators numerically through simulation studies and real data examples. Chapter 4 contains a study of a general linear model with spatial moving average error terms. Asymptotic properties of the shrinkage estimators for the mean parameter vector are investigated. A numerical comparison is carried out and the relative performance of estimators is investigated. Finally, we summarize the findings of the thesis in Chapter 5. Also, some problems for future research are outlined in Chapter 5.

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