A study of robust methods in regression

Abstract

Classical regression theory makes a number of fundamental model assumptions such as that the error terms are independent normally distributed with mean zero and unknown standard deviation. Practical situations arise in which the underlying data generating process deviates to some extent from these model assumptions. In such situations the performance of classical regression techniques may deteriorate considerably. Robust regression techniques has been developed as an alternative to classical regression techniques (such as the ordinary least squares) especially when outliers are present in the data. In simple words an outlier can be said to be a data point which is far from the average value of the rest of the data. Outliers may arise from human-error or may be the result of an unusual but plausible occurrence. In this thesis we shall give a detailed explanation of what constitutes an outlier and show that there are different types of outliers. We shall investigate the effect of outliers on classical regression models and also discuss some diagnostics for identifying these outlying values. The main aim of this dissertation is then to study a number of robust regression methods and compare their performance when applied to contaminated data sets.