Inference from Multinomial Data Based on a MLE-Dominance Criterion

We consider the problem of inference from multinomial data with chances θ, subject to the a-priori information that the true parameter vector θ belongs to a known convex polytope Θ. The proposed estimator has the parametrized structure of the conditional-mean estimator with a prior Dirichlet distribution, whose parameters (s, t) are suitably designed via a dominance criterion so as to guarantee, for any θ ∈ Θ, an improvement of the Mean Squared Error over the Maximum Likelihood Estimator (MLE). The solution of this MLE-dominance problem allows us to give a different interpretation of: (1) the several Bayesian estimators proposed in the literature for the problem of inference from multinomial data; (2) the Imprecise Dirichlet Model (IDM) developed by Walley [13].