Efficient Estimation in Two-Sided Truncated Location Models

Abstract

For a family of two-sided truncated location distributions, based on the generalized Neyman–Pearson lemma, an upper bound for the asymptotic distributions of the absolute deviations of all asymptotically median unbiased estimators for the location parameter is established, upon which the asymptotic efficiency is defined. Except for the cases in which the density has the same values at the truncation points, it is shown that there is no asymptotically median unbiased estimator to be two-sided asymptotically efficient. An adaptive asymptotically weak admissible median unbiased estimator of the location parameter is also constructed.