Optimal Robust M-Estimates of Location

Abstract

We find optimal robust estimates for the location parameter of n independent measurements from a common distribution F that belongs to a contamination neighborhood of a normal distribution. We follow an asymptotic minimax approach similar to Huber's but work with full neighborhoods of the central parametric model including nonsymmetric distributions. Our optimal estimates minimize monotone functions of the estimate's asymptotic variance and bias, which include asymptotic approximations for the quantiles of the estimate's distribution. In particular, we obtain robust asymptotic confidence intervals of minimax length.