An Introduction to Robust Estimation

Abstract

This chapter provides an overview of robust estimation. It is recognized that outliers, which arise from heavy tailed distributions or are simply bad data points because of errors, have an unusually large influence on the least squares estimators. That is, the outliers pull the least squares fit toward them too much; a resulting examination of the residuals is misleading because then they look more like normal ones. Accordingly, robust methods have been created to modify least squares schemes so that the outliers have much less influence on the final estimates. One of the most satisfying robust procedures is that given by a modification of the principle of maximum likelihood. Robust methods have consequently been used successfully in many applications. There has been some evidence that adaptive procedures are of value. The basic idea of adapting is the selection of the estimation procedure after observing the data.