Admissible estimation in an one parameter nonregular family of absolutely continuous distributions

摘要

Consider the problem of estimating under entropy loss an arbitrarily positive, strictly increasing or decreasing parametric function based on a sample of size n in an one parameter noregular family of absolutly continuous distributions with both endpoints of the support depending on a single parameter. We first provide sufficient conditions for the admissibility of generalized Bayes estimator with respect to some specific priors and then treat several examples which illustrate the admissibility of best invariant estimators is some location or scale parameter problems.