Robustness of Clevenson-Zidek-Type Estimators

Abstract

For estimating the means of several independent Poisson distributions, Clevenson and Zidek (1975) were the first to propose a class of estimators that are better than the usual one under the normalized squared error loss (1.1). This class of estimators was subsequently enlarged by others. This article examines the sensitivity of the superiority of the Clevenson-Zidek (CZ)-type means estimators over the usual one with respect to the exactness of the Poisson distribution assumption. It is shown that many of the CZ-type means estimators dominate the usual estimator even when the underlying distributions are negative binomial, whether they are close to the Poisson or not. This broadens the scope of use of CZ-type estimators.

Key Words:

• Clevenson-Zidek estimators
• Poisson
• Negative binomial
• Simultaneous means estimators