Estimation and testing by means of optimally robust statistics

Abstract

It is showed that Hampel's optimal robustification method not only applies to M-estimators, but also to L-estimators and R-estimators. Both location and scale models are considered. By means of influence curves of general statistics, these results are extended to the corresponding tests on one or two samples. The purpose of the present paper is to guide the user of statistical methods by selecting, in each of these classes of statistical procedures, those techniques that are optimally robust. Estimation and testing by means of optimally robust statistics.