Inference from multinomial data based on a MLE-dominance criterion

Abstract

We consider the problem of inference from multinomial data with chances θ, subject to the a-priori information that the true parameter vector θbelongs 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 ε 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]. © 2009 Springer Berlin Heidelberg.