On estimating the mean of the selected uniform population

Let be k independent uniform populations with unknown parameter θ1.Let Y1 denote the largest observation based on a random sample of size n from the i-th population.The population with the largest Y1 is selected. Estimating the mean of the selected population was considered by Vellaisamy, Kumar, and Sharma (1988). They obtained an UMVU estimator and a generalized Bayes estimator for the selected mean. In the case k=2, they showed that the natural estimator is inadmissible w. r. t.(with respect to) the squared error loss L1 , the generalized Bayes estimator is minimax w. r. t. the scale invariant loss L2 and the unbiased estimator can be improved under both loss L1 and L2. In this paper, we consider the same problem and extend most of their results: When k=2, we found an improved estimator of UMVUE among a class of equivariant estimators w.r.t. the L1 loss. For any k≥2, the generalized Bayes estimator is minimax w.r.t. L2, and the UMVUE can be improved under both loss L1 and L2.