Bias Bound for the MiniMax Estimator

The bias bound function of an estimator is an important quantity in order to perform globally robust inference. We show how to evaluate the exact bias bound for the minimax estimator of the location parameter for a wide class of unimodal symmetric location and scale family. We show, by an example, how to obtain an upper bound of the bias bound for a unimodal asymmetric location and scale family. We provide the exact bias bound of the minimum distance/disparity estimators under a contamination neighborhood generated from the same distance.