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

Abstract

In this article we study the simultaneous estimation of the means in Poisson decomposable graphical models. We derive some classes of estimators which improve on the maximum likelihood estimator under the normalized squared losses. Our estimators are based on the argument in Chou [Simultaneous estimation in discrete multivariate exponential families, Ann. Statist. 19 (1991) 314–328.] and shrink the maximum likelihood estimator depending on the marginal frequencies of variables forming a complete subgraph of the conditional independence graph.