Development of model selection criteria for longitudinal data

• 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
• Project Status: Completed (Fiscal Year 2015)
• Budget Amount: ¥3,640,000 (Direct Cost: ¥2,800,000、Indirect Cost: ¥840,000); Fiscal Year 2014: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2013: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2012: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
• Keywords: 経時データ / ランダム係数 / ラプラス近似 / 変数選択 / AIC / 成長曲線モデル / モデル選択規準 / GMANOVAモデル / ランダム効果 / パラレルプロファイルモデル / 共分散構造 / 漸近展開 / 平均構造

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.

Research Products

• [Journal Article] Asymptotic expansions of the null distribution of the LR test statistic for random-effects covariance structure in a parallel pro le model. (2015)
  • Author(s): Y. Inatsu and H. Wakaki
  • Journal Title: Hiroshima Statitical Research Group Technical Report Volume: 15-14 Pages: 1-23
• [Journal Article] A consistency property of the AIC for multivariate linear models when the dimension and the sample size are large (2015)
  • Author(s): H. Yanagihara, H, Wakaki and Y. Fujikoshi
  • Journal Title: Electronic Journal of Statistics Volume: 9 Issue: 1 Pages: 869-897
  • DOI: 10.1214/15-ejs1022
  • Peer Reviewed / Open Access
• [Journal Article] Simple Formula for Calculating Bias-Corrected AIC in Generalized Linear Models. (2014)
  • Author(s): Imori, S., Yanagihara, H. & Wakaki, H.
  • Journal Title: Scand. J. Stat. Volume: in press
  • Peer Reviewed
• [Journal Article] Screening and Selection Methods in High-Dimensional Linear Regression Model. (2014)
  • Author(s): Imori, S., Katayama, S. & Wakaki, H.
  • Journal Title: Hiroshima Statistical Research Group Techinical Report Volume: TR14-01 Pages: 1-21
• [Journal Article] Principal components regression by using generalized principal components analysis (2013)
  • Author(s): Fujiwara, M., Minamidani, T., Nagai, I. and Wakaki, H.
  • Journal Title: J. Japan Statist. Soc. Volume: 43-1 Pages: 57-78
  • NAID: 10031185800
  • Peer Reviewed
• [Presentation] ランダム係数を持つGMANOVAモデルの変数選択規準 (2016)
  • Author(s): 若木 宏文
  • Organizer: 第10回日本統計学会春季集会
  • Place of Presentation: 東北大学
  • Year and Date: 2016-03-05
  • Invited
• [Presentation] ランダム係数を持つGMANOVAモデルの変数選択規準 (2016)
  • Author(s): 若木 宏文
  • Organizer: データ科学シンポジウム2015（科研費）欠測データ解析とモデル選択：生体情報データの統計モデル
  • Place of Presentation: 大阪大学
  • Year and Date: 2016-01-22
• [Presentation] ランダム係数を持つGMANOVAモデルの変数選択規準 (2015)
  • Author(s): 若木 宏文
  • Organizer: 2015 年度科学研究費シンポジウム 大規模複雑データの理論と方法論：最前線の動向
  • Place of Presentation: 筑波大学
  • Year and Date: 2015-11-16
• [Presentation] ランダム係数を持つGMANOVAモデルの変数選択規準 (2015)
  • Author(s): 若木 宏文
  • Organizer: 統計関連学会連合大会
  • Place of Presentation: 岡山大学
  • Year and Date: 2015-09-07
• [Presentation] ランダム係数を持つGMANOVA モデルの 変数選択規準 (2015)
  • Author(s): 若木 宏文
  • Organizer: 日本数学会年会
  • Place of Presentation: 明治大学
  • Year and Date: 2015-03-24
• [Presentation] A Consistency Property of the AIC for Multivariate Linear Models When the Dimension and the Sample Size (2014)
  • Author(s): Hirofumi Wakaki
  • Organizer: The 3rd Institute of Mathematical Statistics Asia Pacific Rim Meeting
  • Place of Presentation: Howard International House, Taipei, Taiwan
  • Year and Date: 2014-06-29 – 2014-07-03
  • Invited
• [Presentation] 平均と共分散行列の構造分析に関する漸近展開とその応用 (2012)
  • Author(s): 松井千代子、若木宏文
  • Organizer: 2012年度統計関連学会連合大会
  • Place of Presentation: 北海道大学
• [Presentation] On the consistency of model selection criteria under a high dimensional framework (2012)
  • Author(s): 若木宏文
  • Organizer: 2012年度統計関連学会連合大会
  • Place of Presentation: 北海道大学
  • Invited
• [Remarks] Hiroshima Statistical Research Group
  • URL: http://www.math.sci.hiroshima-u.ac.jp/stat/TR/index.shtml