Handling Outliers using High-Breakdown and Bounded- Influence Robust Estimation in Linear ' Regression Models

Abstract

This thesis is concerned with robust regression estimation which provides better res!Jlts than OLS in cases in which error distributions are heavy-tailed and/or non-normal or when there are outliers in explanatory and dependent variables.

Robust regression estimators are classified into two large classes:

- The class of bounded- influence estimation methods.

- The class of high-breakdown point estimation methods.

•In the first class, we present method of M-estimation and method of

OM-estimation . In the second class, we present the following methods: Least Median of Squares, Least Trimmed of Squares, Least Trimmed Sum of Absolute Deviations and Penalized Trimmed Squares(using levearage weights and, Mallows weights). Also, a combination of the methods of the two classes is seeked through the

two-stage approach.

A set of algorithms, which approximates solutions of high-breakdown estimation methods in large sample sizes, are presented. In addition, a recent algorithm for handling high-leverage points is presented.