Wild adaptive trimming for robust estimation and cluster analysis

Abstract

AbstractTrimming principles play an important role in robust statistics. However, their use for clustering typically requires some preliminary information about the contamination rate and the number of groups. We suggest a fresh approach to trimming that does not rely on this knowledge and that proves to be particularly suited for solving problems in robust cluster analysis. Our approach replaces the original K‐population (robust) estimation problem with K distinct one‐population steps, which take advantage of the good breakdown properties of trimmed estimators when the trimming level exceeds the usual bound of 0.5. In this setting, we prove that exact affine equivariance is lost on one hand but, on the other hand, an arbitrarily high breakdown point can be achieved by “anchoring” the robust estimator. We also support the use of adaptive trimming schemes, in order to infer the contamination rate from the data. A further bonus of our methodology is its ability to provide a reliable choice of the usually unknown number of groups.