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

Consider independent random samples from \((k\ge 2)\) 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 \(k=2,3.\)