Asymptotic variance estimation in multivariate distributions

Abstract

A version of an asymptotic estimation problem of the unknown variance in a multivariate location-scale parameter family is studied under a general loss function. The asymptotic inadmissibility of the traditional estimator is established. In a particular case we derive an admissible improvement on this estimator.Variance estimation quadratic polynomial in normal means generalized Bayes estimator Brewster-Zidek estimator admissibility