Date of Award
Doctor of Philosophy
In a linear model when the errors follow a normal distribution, least squares methodology is most powerful. However, when the assumption of normality of the error distribution is not met then there exist methods which are more powerful than least squares methods. Rank-based methods form one such class. These methods depend on the selection of a score function [varphi]( u ). The correct choice of [varphi] leads to an optimal (efficient) analysis, but its selection depends on the error distribution which is not known.
In this thesis, we explore different schemes for score selection. Some of these schemes are functions of residuals based on an initial fit of the data. We focuson three such schemes. One is a modification of Hogg's adaptive schemes for simple location model. A second is based on the optimal kernel type estimateof the error density function. While the third selects a score based on a scale criteria. We perform a thorough investigation of each of these schemes and through several extensive monte carlo experiments to determine the validity and power of their associated inference. We also explore several bootstrap procedures for inference for some of these schemes.
Al-Shomrani, Ali A., "A Comparison of Different Schemes for Selecting and Estimating Score Functions Based on Residuals" (2003). Dissertations. 1204.