MATHEMATICAL ENGINEERING TECHNICAL REPORTS Bayesian prediction and model selection for locally asymptotically mixed normal models

The METR technical reports are published as a means to ensure timely dissemination of scholarly and technical work on a non-commercial basis. Copyright and all rights therein are maintained by the authors or by other copyright holders, notwithstanding that they have offered their works here electronically. It is understood that all persons copying this information will adhere to the terms and constraints invoked by each author's copyright. These works may not be reposted without the explicit permission of the copyright holder. Abstract An information criterion for models with the local asymptotic mixed normality (LAMN) is proposed. Since the widely known Akaike's Information Criterion (AIC) is derived based on the local asymptotic normality (LAN), it cannot be directly used to model selection of LAMN models and a criterion for them is required. The proposed criterion for LAMN models is an asymptotically unbiased estimator of the Kullback-Leibler loss of Bayesian prediction. Simulation studies for a mixed normal model, a discretely observed diffusion model and a partially explosive Gaussian AR(2) model are given.