TY  - JOUR
AU  - Hadda, Mechakra 
AU  - Asssia, Chadli 
AU  - Naceur, Tiah 
PY  - 2012
TI  - Bayesian and Maximum Likelihood Solutions:  An Asymptotic Comparison Related to Cost Function
JF  - Journal of Mathematics and Statistics
VL  - 8
IS  - 2
DO  - 10.3844/jmssp.2012.296.310
UR  - https://thescipub.com/abstract/jmssp.2012.296.310
AB  - 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.