Bayesian prediction and model selection for locally asymptotically mixed normal models

Tomonari Sei; Fumiyasu Komaki

doi:10.1016/j.jspi.2006.10.002

Bayesian prediction and model selection for locally asymptotically mixed normal models

Tomonari Sei, Fumiyasu Komaki

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

6 Citations (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	2523-2534
Number of pages	12
Journal	Journal of Statistical Planning and Inference
Volume	137
Issue number	7
DOIs	https://doi.org/10.1016/j.jspi.2006.10.002
Publication status	Published - 2007 Jul 1

Keywords

Bayesian prediction
Information criterion
Kullback-Leibler divergence
Local asymptotic mixed normality
Model selection

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty
Applied Mathematics

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title = "Bayesian prediction and model selection for locally asymptotically mixed normal models",

abstract = "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.",

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AU - Sei, Tomonari

AU - Komaki, Fumiyasu

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N2 - 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.

AB - 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.

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KW - Kullback-Leibler divergence

KW - Local asymptotic mixed normality

KW - Model selection

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