Estimating parameters of a selected Pareto population

Abstract

Let Π 1 , … , Π k be k populations with Π i being Pareto with unknown scale parameter α i and known shape parameter β i ; i = 1 , … , k . Suppose independent random samples ( X i 1 , … , X i n ) , i = 1 , … , k of equal size are drawn from each of k populations and let X i denote the smallest observation of the i th sample. The population corresponding to the largest X i is selected. We consider the problem of estimating the scale parameter of the selected population and obtain the uniformly minimum variance unbiased estimator (UMVUE) when the shape parameters are assumed to be equal. An admissible class of linear estimators is derived. Further, a general inadmissibility result for the scale equivariant estimators is proved.