New types of shrinkage estimators of Poisson means under the normalized squared error loss

ABSTRACT

In estimating p( ⩾ 2) independent Poisson means, Clevenson and Zidek (1975) have proposed a class of estimators that shrink the unbiased estimator to the origin and dominate the unbiased one under the normalized squared error loss. This class of estimators was subsequently enlarged in several directions. This article deals with the problem and proposes new classes of dominating estimators using prior information pertinently. Dominance is shown by partitioning the sample space into disjoint subsets and averaging the loss difference over each subset. Estimation of several Poisson mean vectors is also discussed. Further, simultaneous estimation of Poisson means under order restriction is treated and estimators which dominate the isotonic regression estimator are proposed for some types of order restrictions.

Keywords:

• isotonic regression estimator
• order restriction
• order statistics
• Poisson mean vector

MATHEMATICS SUBJECT CLASSIFCATION:

• 62C99
• 62F10
• 62F30
• 62H12

Acknowledgments

We thank referees and Editor in Chief for careful reading and for valuable suggestions. This work is supported by Grant-in-Aid for Scientific Research (C) No. 26330047, Japan, and also supported by Special Grant-in-Aid for research of Mejiro University.