Bayesian prediction and model selection for locally asymptotically mixed normal models

An information criterion for models with local asymptotic mixed normality (LAMN) is proposed. Since the widely known Akaike's Information Criterion (AIC) is derived on the basis of local asymptotic normality (LAN), it cannot be directly used to model selection of LAMN models, and so a criterion for these models is required. The proposed criterion for LAMN models is an asymptotically unbiased estimator of the Kullback-Leibler risk of Bayesian prediction. We present the results of simulation studies for a mixed normal model, a discretely observed diffusion model and a partially explosive Gaussian AR model.