On Estimation Following Subset Selection from Truncated Poisson Distributions under Stein Loss Function

Abstract

In this paper, we consider the problem of estimating the parameters of a subset selected from p (p ≥ 2) left-truncated Poisson distributions under Stein loss function. Two problems of estimations are considered; average worth and simultaneous estimation. For the average worth, the natural estimator is shown to be positively biased with respect to Stein loss function and the Unique Minimum Risk Unbiased Estimator UMRUE is obtained. For the simultaneous estimation problem, we have shown that the natural estimator is positively biased with respect to Stein loss function and the UMRUE is obtained. The inadmissibility of the natural estimator of the simultaneous estimation is also proved and a class of dominating estimators is obtained. Monte Carlo simulation is undertaken to compute the biases and risks of the two problems of estimation.