Minimum Hellinger Distance Estimates for Parametric Models

Abstract

This paper defines and studies for independent identically distributed observations a new parametric estimation procedure which is asymptotically efficient under a specified regular parametric family of densities and is minimax robust in a small Hellinger metric neighborhood of the given family. Associated with the estimator is a goodness-of-fit statistic which assesses the adequacy of the chosen parametric model. The fitting of a normal location-scale model by the new procedure is exhibited numerically on clear and on contaminated data.