Deviance information criterion for latent variable models and misspecified models

发布时间：2020.05.22

来源：Journal of Econometrics2020,216(2),450-493.

作者：Li,Yong, Yu,Jun and Zeng,tao.

人大经济学院李勇教授学术论文在国际著名计量经济学杂志(Journal of Econometrics)上正式发表。

该论文是与浙江大学经济学院曾涛助理教授以及新加坡管理大学余俊教授共同合作。该篇论文基于著名的模型准则Deviance Information Criterion （DIC, Spiegelhalter et al. 2002), 提出了新的改进模型选择方法。对于经济金融中流行的隐变量模型，该论文首先提出适用于隐变量模型的积分信息准则。同时，针对错误设定的计量模型，文章又提出了一种可以在存在模型误设情况下使用的稳健信息准则。

作者简介：

李勇教授现为经济学院副院长，计量经济学和金融学教授(博导)，长期以来从事贝叶斯金融计量经济学，量化投资，资产配置方面的研究。这是李勇教授第五次在计量经济学顶级期刊Journal of Econometrics发表学术文章。

论文摘要：

Deviance information criterion (DIC) has been widely used for Bayesian model comparison, especially after Markov chain Monte Carlo (MCMC) is used to estimate candidate models. This paper first studies the problem of using DIC to compare latent variable models when DIC is calculated from the conditional likelihood. In particular, it is shown that the conditional likelihood approach undermines theoretical underpinnings of DIC. A new version of DIC, namely DICL, is proposed to compare latent variable models. The large sample properties of DICL are studied. A frequentist justification of DICL is provided. Like AIC, DICL provides an asymptotically unbiased estimator to the expected Kullback-Leibler (KL) divergence between the DGP and a predictive distribution. Some popular algorithms, such as the EM, Kalman and particle filtering algorithms, are introduced to compute DICL for latent variable models. Moreover, this paper studies the problem of using DIC to compare misspecified models. A new version of DIC, namely DICM, is proposed and it can be regarded as a Bayesian version of TIC. A frequentist justification of DICM is provided under misspecification. DICL and DICM are illustrated using asset pricing models and stochastic volatility models.