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Theoretical considerations of model selection method based on a minimization of an information criterion

Research Project

Project/Area Number 25540012
Research Category

Grant-in-Aid for Challenging Exploratory Research

Allocation TypeMulti-year Fund
Research Field Statistical science
Research InstitutionHiroshima University

Principal Investigator

Yanagihara Hirokazu  広島大学, 理学(系)研究科(研究院), 准教授 (70342615)

Co-Investigator(Renkei-kenkyūsha) FUJISAWA HIRONORI  統計数理研究所, 数理・推論研究系, 教授 (00301177)
NINOMIYA YOSHIYUKI  九州大学, マス フォア インダストリ研究所, 准教授 (50343330)
Project Period (FY) 2013-04-01 – 2016-03-31
Project Status Completed (Fiscal Year 2015)
Budget Amount *help
¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000)
Fiscal Year 2015: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2013: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Keywordsモデル選択 / 情報量規準 / 多変量線形回帰モデル / 高次元データ / 一致性 / 大標本高次元漸近理論 / 有効性
Outline of Final Research Achievements

In this research, we study model selection method based on a minimization of an information criterion. There are many information criteria. We evaluate theoretical properties of an information criterion used for model selection by a large sample asymptotic theory such that the sample size goes to infinity and a high-dimensional and large sample asymptotic theory such that the sample size and the dimension of a vector of response variables go to infinity simultaneously. From obtained results, we provide standards of judgment with regard to deciding an information criterion.

Report

(4 results)
  • 2015 Annual Research Report   Final Research Report ( PDF )
  • 2014 Research-status Report
  • 2013 Research-status Report
  • Research Products

    (20 results)

All 2016 2015 2014 2013

All Journal Article (12 results) (of which Int'l Joint Research: 3 results,  Peer Reviewed: 12 results,  Open Access: 4 results,  Acknowledgement Compliant: 2 results) Presentation (8 results) (of which Int'l Joint Research: 1 results,  Invited: 1 results)

  • [Journal Article] Illustration of the Varying Coefficient Model for a Tree Growth Analysis from the Age and Space Perspectives2016

    • Author(s)
      Fukui, K., Yamamura, M. & Yanagihara, H.
    • Journal Title

      FORMATH

      Volume: 15 Issue: 0 Pages: 1-9

    • DOI

      10.15684/formath.15.001

    • NAID

      130005150198

    • ISSN
      2188-5729
    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] A consistency property of the AIC for multivariate linear models when the dimension and the sample size are large2015

    • 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

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Empirical correction to the likelihood ratio statistic for structural equation modeling with many variables2015

    • Author(s)
      Yuan, K.-H., Tian, Y. & Yanagihara, H.
    • Journal Title

      Psychometrika

      Volume: 80 Issue: 2 Pages: 379-405

    • DOI

      10.1007/s11336-013-9386-5

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Conditions for consistency of a log-likelihood-based information criterion in normal multivariate linear regression models under the violation of normality assumption2015

    • Author(s)
      Yanagihara, H.
    • Journal Title

      Journal of the Japan Statistical Society

      Volume: 45 Pages: 21-56

    • NAID

      130005152509

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] Consistency of high-dimensional AIC-type and Cp-type criteria in multivariate linear regression2014

    • Author(s)
      Yasunori Fujikoshi、Tetsuji Sakurai Hirokazu Yanagihara
    • Journal Title

      Journal of Multivariate Analysis

      Volume: 123 Pages: 184-200

    • DOI

      10.1016/j.jmva.2013.09.006

    • Related Report
      2014 Research-status Report
    • Peer Reviewed
  • [Journal Article] Simple Formula for Calculating Bias-Corrected AIC in Generalized Linear Models2014

    • Author(s)
      Imori, S., Yanagihara, H. & Wa kaki, H.
    • Journal Title

      Scandinavian Journal of Statistics

      Volume: (in press) Issue: 2 Pages: 535-555

    • DOI

      10.1111/sjos.12049

    • Related Report
      2014 Research-status Report
    • Peer Reviewed
  • [Journal Article] Jackknife bias correction of the AIC for selecting variables in canonical correlation analysis under model misspecification2014

    • Author(s)
      Hashiyama, Y., Yanagihara, H. & Fujikoshi, Y.
    • Journal Title

      Linear Algebra and its Applications

      Volume: 455 Pages: 82-106

    • DOI

      10.1016/j.laa.2014.04.028

    • Related Report
      2014 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Tests for covariance matrices in high dimension with less sample size2014

    • Author(s)
      Srivastava, M. S., Yanagihara, H. & Kubokawa, T.
    • Journal Title

      Journal of Multivariate Analysis

      Volume: 130 Pages: 289-309

    • DOI

      10.1016/j.jmva.2014.06.003

    • Related Report
      2014 Research-status Report
    • Peer Reviewed
  • [Journal Article] Selecting a shrinkage parameter in structural equation modeling with a near singular covariance matrix by the GIC minimization method2014

    • Author(s)
      Kamada, A., Yanagihara, H., Wakaki, H. & Fukui, K.
    • Journal Title

      Hiroshima Mathematical Journal

      Volume: 44 Pages: 315-326

    • Related Report
      2014 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] Bias-corrected AIC for selecting variables in Poisson regression models.2013

    • Author(s)
      K.Kamo, H.Yanagihara, K.Satoh
    • Journal Title

      Communications in Statistics Theory and Methods

      Volume: 42 Issue: 11 Pages: 1911-1921

    • DOI

      10.1080/03610926.2011.600504

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] A class of cross-validatory model selection criteria2013

    • Author(s)
      Yanagihara, H., Yuan, K.-H., Fujisawa, H. & Hayashi, K.
    • Journal Title

      Hiroshima Mathematical Journal

      Volume: 43 Pages: 149-177

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] Choosing the number of repetitions in the iterative plug-in optimization method for the ridge parameters in multivariate generalized ridge regression2013

    • Author(s)
      Nagai, I., Fukui, K. & Yanagihara, H.
    • Journal Title

      Bulletin of Informatics and Cybernetics

      Volume: 45 Pages: 25-35

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Presentation] Consistent information criterion in normal multivariate linear regression models even under high-dimensionality2015

    • Author(s)
      Yanagihara, H. & Shimodaira, H.
    • Organizer
      The 9th Conference of the Asian Regional Section of the International Association for Statistical Computing
    • Place of Presentation
      National University of Singapore, Singapore
    • Year and Date
      2015-12-17
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Consistent information criterion for normal multivariate linear regression model under high-dimensionality2015

    • Author(s)
      柳原宏和・下平英寿
    • Organizer
      2015年度統計関連学会連合大会
    • Place of Presentation
      岡山大学
    • Year and Date
      2015-09-07
    • Related Report
      2015 Annual Research Report
  • [Presentation] On asymptotically KL loss efficiency of a log-likelihood-based information criterion in high-dimensional normal multivariate linear regression models2014

    • Author(s)
      柳原宏和
    • Organizer
      日本数学会2014年度秋季総合分科会
    • Place of Presentation
      広島大学
    • Year and Date
      2014-09-25 – 2014-09-28
    • Related Report
      2014 Research-status Report
  • [Presentation] On asymptotically KL loss efficiency of a log-likelihood-based information criterion in high-dimensional normal multivariate linear regression models2014

    • Author(s)
      Yanagihara, H.
    • Organizer
      The 3rd. Institute of Mathematical Statistics Asia Pacific Rim Meeting
    • Place of Presentation
      Howard International House, Taipei
    • Year and Date
      2014-06-30 – 2014-07-03
    • Related Report
      2014 Research-status Report
  • [Presentation] A consistency property of the AIC for multivariate linear models when the dimension and the sample size are large2014

    • Author(s)
      Yanagihara, H., Wakaki, H. & Fujikoshi, Y.
    • Organizer
      The 3rd. Institute of Mathematical Statistics Asia Pacific Rim Meeting
    • Place of Presentation
      Howard International House, Taipei
    • Year and Date
      2014-06-30 – 2014-07-03
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] Conditions for consistency of a log-likelihood-based information criterion in high-dimensional multivariate linear regression models under the violation of normality assumption2013

    • Author(s)
      Yanagihara, H.
    • Organizer
      22nd. International Workshop on Matrices and Statistics
    • Place of Presentation
      University of Toronto, Canada
    • Related Report
      2013 Research-status Report
  • [Presentation] Effects of nonnormality on a consistency property of several information criteria for multivariate linear regression models when the dimension and the sample size are large2013

    • Author(s)
      柳原宏和
    • Organizer
      2013年度統計関連学会連合大会
    • Place of Presentation
      大阪大学
    • Related Report
      2013 Research-status Report
  • [Presentation] A consistency property of the AIC for multivariate linear models when the dimension, the sample size and the number of explanation variables are large2013

    • Author(s)
      若木宏文・柳原宏和・藤越康祝
    • Organizer
      2013年度統計関連学会連合大会
    • Place of Presentation
      大阪大学
    • Related Report
      2013 Research-status Report

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Published: 2014-07-25   Modified: 2019-07-29  

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