Simultaneous Estimation of the Means in Some Poisson Log Linear Models

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).

Improving on the maximum likelihood estimators of the means in Poisson decomposable graphical models

“…The last inequality follows from Lemma 3.2 in Hara and Takemura [13]. Thus from the definition of I C(V ,G)…”

“…Hara and Takemura [13] also showed the inadmissibility of the MLE in the three-way decomposable graphical model which corresponds to the decomposable graph in Fig. 1.…”

“…In this paper we extend the results of Hara and Takemura [13] to the general Poisson decomposable model (1) and give the classes of estimators improving on the MLE under the loss function (2). For the generalization we need to prove some basic properties of decomposable graphs.…”

“…Fig. 1 As mentioned in Section 1, Hara and Takemura [13] derived the improved estimators in the three-way model in Fig. 1 …”

“…The model (1) [13] studied the estimation of the means in the Poisson multiplicative models and derived some classes of estimators improving on the MLE by using the argument in [5,4]. Hara and Takemura [13] also showed the inadmissibility of the MLE in the three-way decomposable graphical model which corresponds to the decomposable graph in Fig.…”