A most bias-robust estimate of the location parameter: a general existence theorem

It is well known (HUBER, 1981) that, for symmetrical and unimodal parent distributions, the most asymptotic-bias-robust estimate of the location parameter under e-contamination is the sample median. We show, without any assumptions on symmetry and unimodality, that the most bias-robust estimate exists for every finite sample size. The main result of the paper consists in constructing an appropriate statistical model which differs from that considered by HUBER