Simultaneous Estimation of Several Poisson Parameters Under $K$-Normalized Squared Error Loss

Abstract

In this study, we consider the simultaneous estimation of the parameters of the distributions of $p$ independent Poisson random variables using the loss function $L_k(\lambda, \hat{\lambda}) = \sum (\lambda_i - \hat{\lambda}_i)^2/\lambda^k_i$ for a given positive integer $k$. New estimators are derived, which include the minimax estimators proposed by Clevenson and Zidek (1975), as special cases. The case when more than one observation is taken from some of the variables is considered.