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

Journal of Mathematics and Statistics

Chadli Asssia¹  Mechakra Hadda¹  Tiah Naceur¹ 

关键词: Decision theory cost function;    haar measure;    bayesian solution;    maximum likelihood solution;    topological group;    multivoc function;    measurability;    a priori law;   

DOI  :  10.3844/jmssp.2012.296.310

学科分类：社会科学、人文和艺术（综合）

来源: Science Publications

【 摘 要 】

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.

【 授权许可】

Unknown