Estimating the mean of the selected uniform population

Abstract

Abstract Let πi(i=1,2,…K) be independent U(0,⊝i) populations. Let Yi denote the largest observation based on a random sample of size n from the i-th population. for selecting the best populaton, that is the one associated with the largest ⊝i, we consider the natural selection rule, according to which the population corresponding to the largest Yi is selected. In this paper, the estimation of M. the mean of the selected population is considered. The natural estimator is positively biased. The UMVUE (uniformly minimum variance unbiased estimator) of M is derived using the (U,V)-method of Robbins (1987) and its asymptotic distribution is found. We obtain a minimax estimator of M for K≤4 and a class of admissible estimators among those of the form cYmax. For the case K = 2, the UMVUE is improved using the Brewster-Zidek (1974) Technique with respect to the squared error loss function L1 and the scale-invariant loss function L2. For the case K = 2, the MSE'S of all the estimators are compared for selected values of n and ρ=⊝1/(⊝1+⊝2). Keywords: natural selecton ruleestimation after selectionuniform populationnatural estimatior(U,V)-method of estimationUMVU estimatorgeneralized Bayes estimatoradmissibilityminimaxityimproving on equivariant estimator