Wild adaptive trimming for robust estimation and cluster analysis

Trimming principles play an important role in robust statis- tics. 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 set- ting, 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 estima- tor. 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.