The admissibility of the maximum likelihood estimator for decomposable log-linear interaction models for contingency tables

It is well known that for certain log-linear interaction models for contingency tables, i.e. those that are decomposable, the maximum likelihood estimator can be found explicitly. In this note we will show that in such cases this estimator is admissible. The proof is based on a stepwise Bayes argument and is a generalization of a proof of the admissibility of the maximum likelihood estimator for the usual unconstrained multinomial model. It is then shown that this result is a special case of a result for discrete exponential families.