On umvu estimation following selection

Abstract

In this paper, we obtain some results concerning the UMVUE (uniformly minimum variance unbiased estimator ) of the selected parameter say, for example, the mean. For the squared error loss, the conditions under which the UMVUE is also a UMMSEUE(uniformly minimum mean squared error unbiased estimator), are Investigated, As an application, the UMVUE of θ$sub:I$esub: (or θ$sub:j$esub:), the reciprocal of the natural parameter of the population selected from k independent populations with densities belonging to one parametric continuous exponential family, is also derived. This unifies most of the existing results. The UMVUE of θ$sub:I$esub: is shown to be a UMMSEUE. Some examples are also given.