On double stage minimum discrimination information estimators of the interval constrained normal mean

Abstract

A double sample estimation scheme is considered for lowering the mean square error for the estimator of the normal mean in a region around a prior interval information μ ↦[a,b. The minimum discrimination information(MDI) approach is employed to conduct the scheme. This provides a simple way of specifying the prior interval information about the mean, and also allows to consider a shrinkage type estimator. By means of this approach, double stage MDI estimator and its variants are suggested, and their mean square errors are derived and compared. It is shown that the estimators compare favorably with the previously proposed estimators in terms of mean square error efficiency.