Simultaneous estimation of Poisson means of the selected subset

Let π 1 , π 2 , … , π p be p independent Poisson populations with means λ 1 , … , λ p , respectively. Let {X1,…,Xp} denote the set of observations, where Xi is from π i . Suppose a subset of populations is selected using Gupta and Huangʹs (1975) selection rule which selects π i if and only if X i + 1 ⩾ cX ( 1 ) , where X(1)=max{X1,…,Xp}, and 0 < c < 1 . In this paper, the simultaneous estimation of the Poisson means associated with the selected populations is considered for the k-normalized squared error loss function. It is shown that the natural estimator is positively biased. Also, a class of estimators that are better than the natural estimator is obtained by solving certain difference inequalities over the sample space. A class of estimators which dominate the UMVUE is also obtained. Monte carlo simulations are used to assess the percentage improvements and an application to a real-life example is also discussed.