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Extension of Matrix variate distribution

Research Project

Project/Area Number 18K03428
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Review Section Basic Section 12040:Applied mathematics and statistics-related
Research InstitutionTokyo University of Science

Principal Investigator

Hashiguchi Hiroki  東京理科大学, 理学部第一部応用数学科, 教授 (50266920)

Co-Investigator(Kenkyū-buntansha) 岩下 登志也  東京理科大学, 理工学部教養, 准教授 (20266919)
中川 重和  岡山理科大学, 総合情報学部, 教授 (90248203)
Project Period (FY) 2018-04-01 – 2021-03-31
Project Status Completed (Fiscal Year 2020)
Budget Amount *help
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2020: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2019: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2018: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
Keywordsランダム行列論 / 固有値 / 超幾何関数 / ゾーナル多項式 / 特異行列 / 多変量解析 / 特異ランダム行列 / ウィシャート行列 / 固有値分布 / シミュレーション
Outline of Final Research Achievements

In this research, we establish the following four themes. [Theme 1] Unification of polynomials and special functions that are invariant by a group action required in multivariate distribution theory. [Theme 2] Development of the theory of non-singular matrix variable distribution to the one of a singular case. [Theme 3] Development aimed at robustness from the normal to elliptical populations. [Theme 4] Development to quantization. We were able to publish the results on all these themes.The four themes cannot be divided into independently, but unified each other and produce results through synergistic effects.

Academic Significance and Societal Importance of the Research Achievements

ランダム行列論は,数学的な興味にとどまらず,多変量解析,無線通信,複雑ネットワーク解析などの応用分野でも必要になる理論である.本研究では,特に,特異ランダム行列の正確分布の新しい理論を構築した.また,既存の研究としてある非特異なランダム行列論と,今回の新しい成果との共通点も見出すことができて,統一的に扱うことができることも発見できた.応用上の利点として,多変量解析では多変量分散分析でのロイ型検定統計量の分布の導出により解析条件の緩和や,MIMOの無線通信の理論では,入出力のアンテナの数の大小関係の制限を撤廃し,通信路容量を求めることが可能となったことなどが挙げられる.

Report

(4 results)
  • 2020 Annual Research Report   Final Research Report ( PDF )
  • 2019 Research-status Report
  • 2018 Research-status Report
  • Research Products

    (16 results)

All 2021 2020 2019 2018 Other

All Journal Article (5 results) (of which Peer Reviewed: 5 results,  Open Access: 4 results) Presentation (10 results) (of which Int'l Joint Research: 4 results,  Invited: 1 results) Remarks (1 results)

  • [Journal Article] Heterogeneous hypergeometric functions with two matrix arguments and the exact distribution of the largest eigenvalue of a singular beta-Wishart matrix2021

    • Author(s)
      Shimizu Koki, Hashiguchi Hiroki
    • Journal Title

      Journal of Multivariate Analysis

      Volume: 183 Pages: 104714-104714

    • DOI

      10.1016/j.jmva.2020.104714

    • Related Report
      2020 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Expressing the largest eigenvalue of a singular beta F-matrix with heterogeneous hypergeometric functions2021

    • Author(s)
      Shimizu Koki, Hashiguchi Hiroki
    • Journal Title

      Random Matrices: Theory and Applications

      Volume: 10 Issue: 01 Pages: 2250005-2250005

    • DOI

      10.1142/s2010326322500058

    • Related Report
      2020 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Holonomic properties and recurrence formula for the distribution of sample correlation coefficient2019

    • Author(s)
      Haruto Mura, Hiroki Hashiguchi, Shigekazu Nakagawa, Yoko Ono.
    • Journal Title

      SUT Journal of Mathematics

      Volume: 55

    • NAID

      40022055691

    • Related Report
      2019 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] DISTRIBUTION OF THE LARGEST EIGENVALUE OF AN ELLIPTICAL WISHART MATRIX AND ITS SIMULATION2018

    • Author(s)
      A. Shinozaki, H. Hashiguchi and T. Iwashita
    • Journal Title

      Journal of the Japanese Society of Computational Statistics

      Volume: 30 Issue: 2 Pages: 1-12

    • DOI

      10.5183/jjscs.1708001_244

    • NAID

      130007386273

    • ISSN
      0915-2350, 1881-1337
    • Year and Date
      2018-04-20
    • Related Report
      2018 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] EXACT DISTRIBUTION OF THE LARGEST AND SMALLEST EIGENVALUES OF THE RATIO OF TWO ELLIPTICAL WISHART MATRICES2018

    • Author(s)
      Aya Shinozaki and Hiroki Hashiguchi
    • Journal Title

      Journal of Statistics: Advances in Theory and Applications

      Volume: 19 Issue: 2 Pages: 71-82

    • DOI

      10.18642/jsata_7100121983

    • Related Report
      2018 Research-status Report
    • Peer Reviewed / Open Access
  • [Presentation] 非斉次超幾何関数を用いた特異ベータウィシャート行列の固有値分布論とその応用2020

    • Author(s)
      清水康希, 橋口博樹
    • Organizer
      統計関連連合大会
    • Related Report
      2020 Annual Research Report
  • [Presentation] 行列変数の非斉次超幾何関数による固有値分布の導出とその数値計算2020

    • Author(s)
      清水康希, 橋口博樹
    • Organizer
      確率・統計・行列ワークショップ
    • Related Report
      2020 Annual Research Report
  • [Presentation] 特異楕円ウィシャート行列の固有値の分布について2020

    • Author(s)
      篠崎絢,清水康希,橋口博樹
    • Organizer
      日本計算機統計学会第34回大会
    • Related Report
      2020 Annual Research Report
  • [Presentation] Asymptotic Distribution of Sample Correlation Coefficient Under Elliptical Population2019

    • Author(s)
      Shigekazu Nakagawa, Hiroki Hashiguchi, Yoko Ono
    • Organizer
      Data Science, Statistics & Visualisation
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research
  • [Presentation] 特異ベータウィシャート行列に関する固有値の分布論について2019

    • Author(s)
      橋口博樹,清水康希
    • Organizer
      確率・統計・行列ワークショップ
    • Related Report
      2019 Research-status Report
  • [Presentation] Beta-Wishart ensemble における固有値のガンマ分布近似について2019

    • Author(s)
      那須田亮, 清水康希, 橋口博樹
    • Organizer
      日本計算機統計学会第33 回シンポジウム
    • Related Report
      2019 Research-status Report
  • [Presentation] RMTと情報量基準の融合によるネットワーククラスタリング2019

    • Author(s)
      金子明広, 橋口博樹
    • Organizer
      日本計算機統計学会第33 回シンポジウム
    • Related Report
      2019 Research-status Report
  • [Presentation] Numerical computation for the distribution of the largest eigenvalue under elliptical model2018

    • Author(s)
      Aya Shinozaki
    • Organizer
      Statistical Computing: Challenges and Opportunities in Data Science
    • Related Report
      2018 Research-status Report
    • Int'l Joint Research
  • [Presentation] Approximate distributions of eigenvalues of singular Wishart matrix2018

    • Author(s)
      Koki Shimizu
    • Organizer
      Statistical Computing: Challenges and Opportunities in Data Science
    • Related Report
      2018 Research-status Report
    • Int'l Joint Research
  • [Presentation] Holonomic properties and recurrence formula for the distribution of sample correlation coefficient2018

    • Author(s)
      Haruto Mura
    • Organizer
      Statistical Computing: Challenges and Opportunities in Data Science
    • Related Report
      2018 Research-status Report
    • Int'l Joint Research / Invited
  • [Remarks]

    • URL

      https://www.tus.ac.jp/academics/teacher/p/inde3.php?1f6e#pills-t3-tab4

    • Related Report
      2020 Annual Research Report

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Published: 2018-04-23   Modified: 2022-01-27  

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