Admissible Confidence Interval and Point Estimation for Translation or Scale Parameters

Abstract

Sufficient conditions for admissibility of the best invariant confidence interval for a translation or scale parameter are given, for a very wide class of loss functions. These conditions result by adapting a theorem of L. D. Brown [2]. Simpler sufficient conditions are found for a subclass of loss functions of special interest. The subclass of losses involves three components. One concerned with coverage of the true value, another concerned with the distance from the interval end points to the true parameter, and a third concerned with length of the interval. Such a loss function unifies confidence interval and point estimation in the sense that if an optimality property holds for all loss functions in the subclass, then the optimality property holds for typical confidence interval problems and typical point estimation problems.