Robust multivariate location estimation, admissibility, and shrinkage phenomenon

Abstract

Estimators of multivariate location parameters are generally dominated, in finite as well as asymptotic setups, by suitable shrinkage versions, and hence are inadmissible; such shrinkage estimators may not be admissible either. This feature is shared by maximum likelihood and many robust estimators. The interplay of robustness, admissibility and shrinkage phenomenon in some general multivariate location models (not necessarily elliptically or spherically symmetric) is illustrated and applied to Huber-type contamination models.