Strong Admissibility of a Set of Confidence Intervals for the Mean of a Finite Population

Abstract

In a previous paper the admissibility was proved of a generalized version of the confidence sets, commonly used in practice, which are based on the sample mean and the sample standard deviation. A stronger definition of admissibility is obtained, if instead of the length of the interval for each individual observable sample $s$, only the expected length for all samples together for each $x \in R_N$, is taken into consideration for defining the permissible alternatives to the given set of confidence intervals. This stronger definition corresponds exactly to the definition of strong admissibility formulated by the author (1969) for confidence procedures for the parameter $\theta$ in a uni- or multivariate population. Using the stronger definition it is shown that confidence sets centered at the sample mean but having a fixed length are strongly admissible. The question of the strong admissibility of the usual confidence intervals with length proportional to the sample deviation remains open.