Abstract
Beran (1977) showed that, under certain restrictive conditions, the minimum distance estimator based on the Hellinger distance (MHDE) between a projection model density and a nonparametric sample density is an exception to the usual perception that a robust estimator cannot achieve full efficiency under the true model. We examine the MHDE in the case of estimation of the mixing proportion in the mixture of two normals. We discuss the practical feasibility of employing the MHDE in this setting and examine empirically its robustness properties. Our results indicate that the MHDE obtains full efficiency at the true model while performing comparably with the minimum distance estimator based on Cramer-von Mises distance under the symmetric departures from component normality considered.
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