Asymptotic Properties of Bayesian Type Estimators When It Is Not Assumed the Hessian Matrices of Contrast Functions Converge

• Activity Number: 503
• Type: Contributed
• Date/Time: Wednesday, August 6, 2014 : 10:30 AM to 12:20 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Yoichi Miyata*+
• Companies: Takasaki City University of Economics
• Keywords: Bayesian type estimators ; Strong consistency ; Asymptotic normality ; Heterogeneous AR(1) models

Abstract

Typically, consistency and asymptotic normality of Bayes estimators are proved via the Bernstein-von Mises theorem, and hence it is necessary to assume that the Hessian of loglikelihood function converges to a positive definite matrix independent of the sample size. In this talk, we give sufficient conditions for strong consistency and asymptotic normality of the Bayesian type estimators under possibly misspecified models without assuming that contrast functions and their Hessian matrices converge. Especially, we describe the asymptotic properties when the stochastic process is $\alpha$-mixing but not necessarily stationary, e.g., heterogeneous AR(1) models. These results are closely related to those of White and Domowitz (1984), which gives sufficient conditions for strong consistency and asymptotic normality of minimum contrast estimators in the non-i.i.d. case.