Minimum Hellinger Distance Estimation for Normal Models

摘要

A robust estimator introduced by Beran (1977a, 1977b) which is based on theminimum Hellinger distance between a projection model density and a nonparametric sample density is studied empirically. An extensive simulation provides an estimate of the small sample distribution and supplies empirical evidence of the estimator performance for a normal location-scale model. Empirical robustness is also investigated, with performance competitive with that obtained from M-estimator and Cramer-von Mises minimum distance estimators. The minimum Hellinger distance estimator is shown to be an exception to the usual perception that a robust estimator cannot achieve full efficiency. Beran also introduced a goodness-of-fit statistic, H squared, based on the minimized Hellinger distance between a member of a parametric family of densities and a nonparametric density estimate. We investigate the statistic H (the square root H squared) as a test for normality when both location and scale are unspecified. Empirically derived critical values are given which do not require extensive tables. The power of the statistic H is compared with four other widely used tests for normality. Keywords: Minimum distance, Robustness, Efficiency, Nonparametric. (kr)