ESTIMATION OF THE FUNCTIONS OF PARAMETERSOF THE SELECTED SUBSETUNDER STEIN LOSS FUNCTION

摘要

Let Π_1,..., Π_p be p (p ≥ 2) independent left-truncated generalized Poisson pop-ulations with functions of parameters h(θ_1), ··· , h(θ_p), respectively, where the form of h is known while the parameters θ_i , ··· , θ_p are unknown. For each 1 ≤ i ≤ p, denotes the sum of n independent observations from the population H,. Suppose a subset of random size includes the best population (the one associated with the small-est θ_i) from the p populations is selected using the following modified selection rule (Gupta, Leong and Wong (1978)): choose _i in the subset iff Z_i≤ c(Z_((p))+1) where Z_((p)) = min(Z_1 , ··· ,Z_p) and c ≥ 1. In this paper, we consider the problem of estimating the functions of parameters of the selected subset 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 negatively biased with respect to Stein loss function and the UMVUE is obtained using Robbin's (1988) UV method of estimation. The inadmissibility of the natural estimator is proved by constructing a class of dominating estimators. For the simultaneous estimation, the inadmissibility of the natural estimator proved and a class of dominating estimators is obtained.