Bayesian and Maximum Likelihood Solutions: An Asymptotic Comparison Related to Cost Function

Abstract

Problem statement: Wald showed that the minimax solution is the Bayesian solution with respect to the law a priori the worst. We try to establish a similar result by comparing the Bayesian solution and the solution of maximum likelihood when the parameter space is a compact metrizable group. Approach: we take as a priori law Haar measure because we reduce the problem by invariance. We construct a sequence of cost functions for which we obtain a sequence of solutions Bayesian which converges to the solution of the maximum likelihood. Results: We show that both solutions are asymptotically equal. Conclusion/Recommendation: The generalization when the parameter space is a local compact group.