Development of model selection criteria for longitudinal data

2015 Fiscal Year Final Research Report

• Project/Area Number: 24500343
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Statistical science
• Research Institution: Hiroshima University
• Principal Investigator: Wakaki Hirofumi 広島大学, 理学(系)研究科(研究院), 教授 (90210856)
• Project Period (FY): 2012-04-01 – 2016-03-31
• Keywords: 経時データ / ランダム係数 / ラプラス近似 / 変数選択 / AIC

Outline of Final Research Achievements

We derived an asymptotic expansion formula of the bias of the naive estimator by the maximum log-likelihood function for the risk of the predicted distribution based on Kullback-Leibler divergence for a random coefficient model with using the Laplace's method. We prove that the order of the error term of this approximation formula is uniform with respect to the unknown parameters. We proposed a bias-modified AIC criterion of which the order of bias is o(1/n) where n is the sample size.
We also treated a mixed effects model with two random coefficients. the maximum likelihood estimators of the unknown parameters are derived. We represent the bias of the predicted distribution so that we can apply the Laplace's method. However, it is not clear whether the order of the error term is uniform with respect to the unknown parameters.

Free Research Field

数理統計学