Title

Absolute penalty and shrinkage estimation strategies in linear and partially linear models with correlated errors

Date of Award

2013

Degree Type

Dissertation

Degree Name

Ph.D.

Department

Mathematics and Statistics

First Advisor

S. Ejaz Ahmed

Keywords

Statistics

Rights

CC BY-NC-ND 4.0

Abstract

In this dissertation we propose shrinkage estimators and absolute penalty estimators (APEs) in linear models, partially linear models (PLM) and quasi-likelihood models. We study the asymptotic properties of shrinkage estimators both analytically and through simulation studies, and compare their performance with APEs. In Chapter 2, we propose shrinkage estimators for a multiple linear regression with first order random coefficient autoregressive (RCAR(1)) error term. We also present two APEs for this models which are modified versions of lasso and adaptive lasso estimators. We compare the performance of shrinkage estimators and APEs through the mean squared error criterion. Monte Carlo studies were conducted to compare the estimators in two situations: when p > n and when p < n. A data example is presented to illustrate the usefulness of the suggested methods. In Chapter 3, we develop shrinkage estimators for a PLM with RCAR(1) error term. The nonparametric function is estimated using a kernel function. We also compare the performance of shrinkage estimators with a modified version of lasso for correlated data. Monte Carlo studies were conducted to compare the behavior of the proposed estimators. A data example is presented to illustrate the application of the suggested methods. In Chapter 4, we propose pretest and shrinkage estimators for quasi-likelihood models. We investigate the asymptotic properties of these estimators both analytically and through simulation studies. We also apply a lasso estimator and compare its performance with the other proposed estimators.