Further Developments on the Robustness of Clevenson—Zidek-Type Means Estimators

Abstract

Tsui (1984) showed that many Clevenson—Zidek-type Poisson means estimators are better than the usual estimator under the normalized squared error loss (1.1), even when the underlying distributions are negative binomial. This article shows that this dominance result is still true when the underlying distributions belong to a much larger class of distributions. This class includes all mixtures of Poisson distributions, and hence the negative binomial result is a very special case.

Key Words:

• Poisson
• Mixtures of Poisson distributions
• Simultaneous means estimators