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

Journal of Mathematics and Statistics

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

Mechakra Hadda, Chadli Asssia and Tiah Naceur

DOI : 10.3844/jmssp.2012.296.310

Journal of Mathematics and Statistics

Volume 8, Issue 2

Pages 296-310

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.

Copyright

© 2012 Mechakra Hadda, Chadli Asssia and Tiah Naceur. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.