Concepts and Suggestions for Robust Regression Analysis

Theory: Robust methods for regression yield parameter estimates that are insensitive to small departures in the data from the assumed model. A review of some basic ideas of robust estimation focuses on a class of techniques called M-estimators that discount the impact of outlying observations. Methods: These ideas are extended to three practically important areas: (1) some simple methods for inference for robust estimators are described; (2) a more general class of robust estimators for generalized linear models is then introduced; (3) the high breakdown least median of squares method is presented. Results: Applications from comparative and American politics illustrate ideas in these areas.