J. Japan Statist. Soc., Vol. 36 (No. 1), pp. 17-36, 2006

Simultaneous Estimation of the Means in Some Poisson Log Linear Models

Hisayuki Hara and Akimichi Takemura

Abstract. In this article we study the simultaneous estimation of the Poisson means in J-way multiplicative models and a decomposable model for three-way layouts. The estimators which improve on the maximum likelihood estimators under the normalized squared error losses are provided for each model. The proposed estimators correspond to the ones by Clevenson and Zidek (1975), Tsui and Press (1982) and Chou (1991).

Key words and phrases: Bayes estimation, decomposable Poisson model, multiplicative Poisson model, shrinkage estimation, unbiased estimation of risk difference.

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