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New Development of Statistical Theory in Multivariate Data Analysisand Its Applications

Research Project

Project/Area Number 22500259
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Statistical science
Research InstitutionHiroshima University

Principal Investigator

FUJIKOSHI Yasunori  広島大学, 大学院・理学研究科, 名誉教授 (40033849)

Co-Investigator(Kenkyū-buntansha) YANAGIHARA Hirokazu  広島大学, 大学院・理学研究科, 准教授 (70342615)
Project Period (FY) 2010 – 2012
Project Status Completed (Fiscal Year 2012)
Budget Amount *help
¥3,380,000 (Direct Cost: ¥2,600,000、Indirect Cost: ¥780,000)
Fiscal Year 2012: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2011: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2010: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Keywordsモデル選択 / 多変量回帰モデル / 成長曲線モデル / 正準相関分析 / 判別分析 / 高次元漸近理論 / 多項ロジット回帰 / 環境データ分析 / モデル選択問題 / 経時データ分析問題 / 高次元問題 / 多変量モデルの選択 / プロファイル分析法 / ランダム係数モデル / 平行性モデル / 誤差限界 / 情報量規準 / 平滑化 / 正規対称行列データ
Research Abstract

In this project we tackled the following important problems in multivariate statistical analysis: (1) Development of statistical inference in quantification methods, (2) Proposals of high-dimensional model selection criteria and study on their properties, (3) Development of statistical inference in analysis of repeated measurement data, (4) Development of statistical inference for multivariate non-linear models, (5) Development of high-dimensional statistical methods and asymptotic theory. Especially, we proposed high-dimensional AIC, etc. Further, we showed that they have consistency property.

Report

(4 results)
  • 2012 Annual Research Report   Final Research Report ( PDF )
  • 2011 Annual Research Report
  • 2010 Annual Research Report
  • Research Products

    (29 results)

All 2013 2012 2011 2010

All Journal Article (13 results) (of which Peer Reviewed: 13 results) Presentation (10 results) (of which Invited: 1 results) Book (6 results)

  • [Journal Article] High-dimensional AICs for selection of variables in discriminant analysis2013

    • Author(s)
      Sakurai Tetsuro 、 Nakata Takashi 、Fujikoshi Yasunori
    • Journal Title

      Sankhya

      Volume: 75 Pages: 1-25

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] A variable selection criteria for two sets of principal component scores in principal canonical correlation analysis2013

    • Author(s)
      Ogura Toru 、 Fujikoshi Yasunori 、Sugiyama Takakazu
    • Journal Title

      Communications in Statistics=Theory and Methods

      Volume: 42 Pages: 1-18

    • Related Report
      2012 Annual Research Report 2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] High-dimensional AICs for selection of variables in discriminant analysis.2013

    • Author(s)
      Sakurai, T.
    • Journal Title

      Sankhya, A

      Volume: 75 Issue: 1 Pages: 1-25

    • DOI

      10.1007/s13171-013-0025-0

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Bias-corrected AIC for selecting variables in multinomial logistic regression models2012

    • Author(s)
      Yanagihara Hirokazu
    • Journal Title

      Linear Algebra and Its Applications

      Volume: 436 Pages: 4329-4341

    • Related Report
      2012 Annual Research Report 2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Iterative bias correction of the cross-validation criterion2012

    • Author(s)
      Yanagihara Hirokazu、 Fujisawa Hironori
    • Journal Title

      Scandinavian Journal of Statistics

      Volume: 39 Pages: 116-130

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Iterative bias-correction of the cross-validation criterion2012

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

      Scandinavian Journal of Statistics

      Volume: 39 Issue: 1 Pages: 116-130

    • DOI

      10.1111/j.1467-9469.2011.00754.x

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] LR tests for two hypotheses in profile analysis of growth curve data2011

    • Author(s)
      Seo Takashi、 Sakurai Tomoko、 Fujikoshi Yasunori
    • Journal Title

      SUT Journal of Mathematics

      Volume: 47 Pages: 105-118

    • Related Report
      2012 Final Research Report 2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] High-dimensional asymptotic distribution of test statistic for multivariate linear hypothesis in random-coefficient model2011

    • Author(s)
      Sakurai Tetsuro 、 Igeta Masataka 、Fujikoshi Yasunori
    • Journal Title

      Journal of Combinatorics 、Information and System Sciences

      Volume: 36 Pages: 49-62

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Prediction error criterion for selecting variables in a linear regression model、Ann. Inst. Statist2011

    • Author(s)
      Fujikoshi Yasunori
    • Journal Title

      Math.

      Volume: 63 Pages: 387-403

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] High-dimensional asymptotic distribution of test statistic for multivariate linear hypothesis in random-coefficient model2011

    • Author(s)
      Sakurai, T., Igeta, M., Fujikoshi, Y.
    • Journal Title

      Journal of Combinatorics, Information and System Sciences

      Volume: 36 Pages: 49-62

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Prediction error criterion for selecting variables in a linear regression model2011

    • Author(s)
      Fujikoshi, Y., et al.
    • Journal Title

      Ann.Inst.Statist.Math.

      Volume: 63 Pages: 387-403

    • NAID

      40018765529

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A non-iterative optimization method for smoothness in penalized spline regression2011

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

      Statistics and Computing

      Volume: (未定 掲載決定)

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] High-dimensional asymptotic expansion of LR statistic for testing the intraclass correlation structure and its error bound2010

    • Author(s)
      Kato Nohiro、 Yamada Tomoyuki、 Fujikoshi Yasunori
    • Journal Title

      Journal of Multivariate Analysis

      Volume: 101 Pages: 101-112

    • Related Report
      2012 Final Research Report 2010 Annual Research Report
    • Peer Reviewed
  • [Presentation] 高次元モデル選択規準2013

    • Author(s)
      藤越康祝
    • Organizer
      第7回統計学会春季集会
    • Place of Presentation
      学習院大学
    • Year and Date
      2013-03-03
    • Related Report
      2012 Annual Research Report 2012 Final Research Report
  • [Presentation] On the consistency of model selection criteria under a high dimensional Framework2012

    • Author(s)
      Fujikoshi Yasunori
    • Organizer
      International Conference on Advances in InterdisciplinaryStatistics and Combinatorics
    • Place of Presentation
      ノースカロライナ大学グリーンズボロ校、米国
    • Year and Date
      2012-10-07
    • Related Report
      2012 Final Research Report
  • [Presentation] High-dimensional approximations of the characteristic roots and vectors in discriminant analysis and and canonical correlation analysis2012

    • Author(s)
      Fujikoshi Yasunori
    • Organizer
      第2回環太平洋地域数理統計会議
    • Place of Presentation
      筑波国際会議場
    • Year and Date
      2012-07-04
    • Related Report
      2012 Annual Research Report 2012 Final Research Report
  • [Presentation] On the consistency of model selection criteria under a high dimensional framework2012

    • Author(s)
      Fujikoshi, Y.
    • Organizer
      International Conference on Advances in Interdisciplinary Statistics and Combinatorics
    • Place of Presentation
      University of North Carolina, Breensboro
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] 判別分析および正準相関分析における固有値と固有ベクトルの高次元漸近分布2011

    • Author(s)
      藤越康祝
    • Organizer
      2011 年度統計関連学会連合大会
    • Place of Presentation
      九州大学
    • Year and Date
      2011-09-05
    • Related Report
      2012 Final Research Report
  • [Presentation] 判別分析および正準相関分析における固有値と固有ベクトルの高次元漸近分布2011

    • Author(s)
      藤越康祝
    • Organizer
      2011年度統計関連学会連合大会
    • Place of Presentation
      九州大学
    • Year and Date
      2011-09-05
    • Related Report
      2011 Annual Research Report
  • [Presentation] A comparison of three estimators in GMANOVA model when the sample size is fewer than the dimension、The 9th Tartu Conference on Multivariate Statistics2011

    • Author(s)
      Yanagihara Hirokazu
    • Organizer
      The 20th International Workshop on Matrices and Statistics
    • Place of Presentation
      Tartu University, Estonia
    • Year and Date
      2011-06-29
    • Related Report
      2012 Final Research Report
  • [Presentation] A comparison of three estimators in GMANOVA model when the sample size is fewer than the dimension2011

    • Author(s)
      Yanagihara, H., Srivastava, M.S.
    • Organizer
      The 9th Tartu Conference on Multivariate Statistics & The 20th International Workshop on Matrices and Statistics
    • Place of Presentation
      Tartu University, Estonia(招待講演)
    • Year and Date
      2011-06-29
    • Related Report
      2011 Annual Research Report
  • [Presentation] 正規対称行列変数に関する推測統計量の漸近的精密化2010

    • Author(s)
      藤越康祝
    • Organizer
      2010 年度統計関連学会連合大会
    • Place of Presentation
      早稲田大学
    • Year and Date
      2010-09-07
    • Related Report
      2012 Final Research Report
  • [Presentation] 正規対称行列変数に関する推測統計量の漸近的精密化2010

    • Author(s)
      藤越康祝
    • Organizer
      2010年度統計関連学会連合大会
    • Place of Presentation
      早稲田大学、東京
    • Year and Date
      2010-09-07
    • Related Report
      2010 Annual Research Report
  • [Book] 多変量モデルの選択2012

    • Author(s)
      藤越康祝、杉山高一
    • Total Pages
      208
    • Publisher
      朝倉書店
    • Related Report
      2012 Final Research Report
  • [Book] R により環境データの統計分析2012

    • Author(s)
      吉本敦、加茂憲一、柳原宏和
    • Total Pages
      202
    • Publisher
      朝倉書店
    • Related Report
      2012 Final Research Report
  • [Book] Rにより環境データの統計分析2012

    • Author(s)
      吉本敦・加茂憲一・柳原宏和
    • Total Pages
      202
    • Publisher
      朝倉書店
    • Related Report
      2011 Annual Research Report
  • [Book] 質的データの判別分析:数量化 2 類2011

    • Author(s)
      菅民郎、藤越康祝
    • Total Pages
      264
    • Publisher
      現代数学社
    • Related Report
      2012 Final Research Report
  • [Book] 多変量モデルの選択2011

    • Author(s)
      藤越康祝・杉山高一
    • Total Pages
      208
    • Publisher
      朝倉書店
    • Related Report
      2011 Annual Research Report
  • [Book] 質的データの判別分析:数量化2類2011

    • Author(s)
      菅民郎、藤越康祝
    • Total Pages
      264
    • Publisher
      現代数学社
    • Related Report
      2010 Annual Research Report

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Published: 2010-08-23   Modified: 2019-07-29  

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