Robust Estimation

Robust estimation is a topic of robust statistics. Robust statistics addresses the problem of making estimates that are insensitive to small changes in the basic assumptions of the statistical models employed. This is useful to separate the contribution of the tails from the contribution of the body of the data. Hence, robust statistics and classical nonrobust statistics are complementary. This chapter discusses methods for robust estimation, with particular emphasis on the robust estimation of regressions. In particular, it introduces robust regression estimators and robust regression diagnostics. It also introduces the concepts of qualitative and quantitative robustness of estimators. Estimators are functions of the sample data. They are called resistant if they are insensitive to change in one single observation.