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We study asymptotic behaviors of Bayes type estimators and give sufficientconditions to obtain asymptotic limit distribution of estimation error. Weassume polynomial type large deviation inequalities and prove asymptoticequivalence of estimation error of Bayes type estimator and that of M-estimatorby the virtue of Ibragimov-Has'minskii's theory. The results can be applied toseveral statistical models of diffusion processes and jump diffusion processes.In this paper, we focus on application to a statistical model of an ergodicdiffusion process and give asymptotic normality and convergence of moments ofthe Bayes type estimator with a general loss function.

On Asymptotic Properties of Bayes Type Estimators with General Loss Functions