On the Selection of the Underlying Distribution and Adaptive Estimation

Abstract

In our approach to adaptive inference, selection of the true underlying family of distributions is needed. A Bayesian selection rule, which is based on non-informative priors for the parameters, and a multiple decision solution, that maximizes the weighted sum of the probabilities of correct selection, are presented; both of these yield a decision rule of the same form. A modified maximum likelihood solution is also given and is used to construct an adaptive estimate of the location of a symmetric distribution. By a Monte Carlo study, it is found that this adaptive estimator compares most favorably to more standard estimators.