inadmissibility of the maximum likelihood estimator of the inverse gaussian mean

Abstract

The traditional estimator of the mean of an inverse Gaussian distribution is the sample mean, which is the maximum likelihood estimator and the best unbiased estimator. In this paper alternative estimators of this parameter are introduced. They are shown to improve under quadratic loss on the sample mean which establishes the inadmissibility of the latter. To illustrate the extent of the improvement some numerical results are given.