統計学輪講（第２１回）

統計学輪講（第21回）
日時      2012年11月27日(火)    14時50分～15時40分
場所      経済学部新棟３階第３教室
講演者    川久保友超 (経済M2)
演題      Comparison of Information Criteria for Predictive Variable
Selection in Linear Mixed Models

概要
In the problem of selecting the explanatory variables and the random
effects in the linear mixed models, we suggest 2 new criteria and compare
them with conventional ones: the marginal AIC (mAIC) and the conditional
AIC (cAIC).

The cAIC can be interpreted as measuring the prediction error of the
plug-in predictive density in the context of the Bayesian prediction
problem. In this framework, it is known that the Bayesian predictive
density improves on the plug-in predictive density. Thus, we suggest the
information criterion based on the Bayesian predictive density, which is
here called the Bayesian predictive AIC (bpAIC). We also suggest the
conditional predictive information criterion (cPIC), which uses the
conditional predictive density directly instead of the plug-in predictive
density.

The penalty (bias correction) terms in these criteria are estimated by
Taylor series expansions and paremetric bootstrap methods.

Finally, the numerical performance of the proposed information criteria are
investigated through simulation studies.