Estimating moments of a selected Pareto population under asymmetric scale invariant loss function

Abstract

Consider independent random samples from (k ≥ 2) Pareto populations with the same known shape parameter but different scale parameters. Let X i be the smallest observation of the ith sample. The natural selection rule which selects the population associated with the largest X i is considered. In this paper, we estimate the moments of the selected population under asymmetric scale invariant loss function. We investigate risk-unbiased, consistency and admissibility of the natural estimators for the moments of the selected population. Finally, the risk-bias's and risks of the natural estimators are numerically computed and compared for k = 2, 3.