Robust Regression Methods and Model Selection

Abstract

Robust statistics deals with approximate statistical models and develops statistical techniques that are resistant and reliable in the presence of small deviations from assumed models. This chapter provides an overview of basic concepts and tools of robust statistics. In the first part we focus on regression models and discuss the most important classes of robust procedures for estimation and inference, which have been developed in the past two decades. The aim is not to provide a complete list of techniques but rather to highlight the basic ideas and discuss the statistical and computational properties of the most important robust methods for regression.

The second part is devoted to robust model selection. We present robust versions of parametric model selection criteria as well as nonparametric techniques based on cross-validation.