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Statistical analysis of rankings and hyperplane arrangements

Research Project

Project/Area Number 22540134
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field General mathematics (including Probability theory/Statistical mathematics)
Research InstitutionNagoya University (2011-2012)
Okayama University (2010)

Principal Investigator

KAMIYA Hidehiko  名古屋大学, 経済学研究科, 教授 (50300687)

Project Period (FY) 2010 – 2012
Project Status Completed (Fiscal Year 2012)
Budget Amount *help
¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
Fiscal Year 2012: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2011: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2010: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Keywords統計数学
Research Abstract

In the general setting of the theory of hyperplane arrangements, we studied properties of a hyperplane arrangement which is stable under the action of a Coxeter group and obtained some results such as the number of the orbits of the chambers of this arrangement. Moreover, applying the general results to the problem of rankings, we found the exact number of essentially different ranking patterns which can be generated by the unfolding model of codimension one. Applying the general results to another problem, we also investigated properties of a preference order called semiorder. Besides, we defined a family of distributions and examined its properties in the general setting of group invariance.

Report

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

    (21 results)

All 2012 2011 2010 Other

All Journal Article (9 results) (of which Peer Reviewed: 5 results) Presentation (12 results)

  • [Journal Article] Arrangements stable under the Coxeter groups, Configuration Spaces: Geometry, Combinatorics and Topology2012

    • Author(s)
      H. Kamiya, A. Takemura and H. Terao
    • Journal Title

      CRM Series

      Volume: 14 Pages: 327-354

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Null robustness and marginal equivalence associated with orbital decompositions2012

    • Author(s)
      紙屋英彦
    • Journal Title

      「研究集会数理統計学の沃野」報告集

      Pages: 97-100

    • Related Report
      2012 Final Research Report
  • [Journal Article] Application of arrangement theory to unfolding models, Arrangements of Hyperplanes---Sapporo 20092012

    • Author(s)
      H. Kamiya, A. Takemura and N. Tokushige
    • Journal Title

      Advanced Studies in Pure Mathematics

      Volume: Vol. 62 Pages: 399-415

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Arrangements stable under the Coxeter groups2012

    • Author(s)
      Hidehiko Kamiya
    • Journal Title

      CRM Series, Configuration Spaces: Geometry, Combinatorics and Topology

      Volume: 14 Pages: 327-354

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Null robustness and marginal equivalence associated with orbital decompositions2012

    • Author(s)
      紙屋英彦
    • Journal Title

      「研究集会 数理統計学の沃野」 報告集

      Volume: - Pages: 97-100

    • Related Report
      2012 Annual Research Report
  • [Journal Article] Ranking patterns of unfolding models of codimension one2011

    • Author(s)
      H. Kamiya, A. Takemura and H. Terao
    • Journal Title

      Advances in Applied Mathematics

      Volume: Vol. 47 Pages: 379-400

    • NAID

      120003207598

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Ranking patterns of unfolding models of codimension one2011

    • Author(s)
      Hidehiko Kamiya, A. Takemura and Hiroaki Terao
    • Journal Title

      Advances in Applied Mathematics

      Volume: 47 Issue: 2 Pages: 379-400

    • DOI

      10.1016/j.aam.2010.11.002

    • NAID

      120003207598

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Arrangements stable under the Coxeter groups, Version 22011

    • Author(s)
      Hidehiko Kamiya, Akimichi Takemura, Hiroaki Terao
    • Journal Title

      arXIv.org

    • Related Report
      2011 Annual Research Report
  • [Journal Article] Arrangements stable under the Coxeter groups2011

    • Author(s)
      Hidehiko Kamiya, Akimichi Takemura, Hiroaki Terao
    • Journal Title

      Mathematical Engineering Technical Reports

      Volume: 2011-10 Pages: 1-19

    • Related Report
      2010 Annual Research Report
  • [Presentation] Null robustness and marginal equivalence associated with orbital decompositions2012

    • Author(s)
      紙屋英彦
    • Organizer
      科研費研究集会「数理統計学の沃野」
    • Place of Presentation
      慶應義塾大学
    • Year and Date
      2012-11-23
    • Related Report
      2012 Final Research Report
  • [Presentation] Rankings and hyperplane arrangements2012

    • Author(s)
      紙屋英彦
    • Organizer
      Forum on Probability, Statistics, Algebra and Combinatorics
    • Place of Presentation
      名古屋大学理学部
    • Year and Date
      2012-07-28
    • Related Report
      2012 Final Research Report
  • [Presentation] Ranking patterns of unfolding models of codimension one2012

    • Author(s)
      H. Kamiya, A. Takemura and H. Terao
    • Organizer
      The 2nd Institute of Mathematical Statistics Asia Pacific Rim Meeting (IMS-APRM 2012)
    • Place of Presentation
      Tsukuba International Congress Center
    • Year and Date
      2012-07-03
    • Related Report
      2012 Final Research Report
  • [Presentation] Application of arrangement theory to unfolding models2011

    • Author(s)
      紙屋英彦,竹村彰通,徳重典英
    • 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 2011 Annual Research Report
  • [Presentation] Ranking patterns of unfolding models of codimension one (Joint work with A. Takemura and H. Terao)2011

    • Author(s)
      紙屋英彦
    • Organizer
      名古屋統計セミナ・組合せ論セミナー
    • Place of Presentation
      名古屋大学 情報科学研究科
    • Year and Date
      2011-06-17
    • Related Report
      2012 Final Research Report
  • [Presentation] Ranking patterns of unfolding models of codimension one2010

    • Author(s)
      紙屋英彦,竹村彰通,寺尾宏明
    • Organizer
      科学研究費研究集会「計算代数と数理統計学の新たな展開」
    • Place of Presentation
      埼玉県さいたま市 大宮ソニックシティー
    • Year and Date
      2010-11-16
    • Related Report
      2012 Final Research Report
  • [Presentation] Ranking patterns of unfolding models of codimension one2010

    • Author(s)
      紙屋英彦,竹村彰通,寺尾宏明
    • 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
      2010-09-08
    • Related Report
      2012 Final Research Report
  • [Presentation] Ranking patterns of unfolding models of codimension one2010

    • Author(s)
      紙屋英彦, 竹村彰通, 寺尾宏明
    • 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
      2010-09-08
    • Related Report
      2010 Annual Research Report
  • [Presentation] 選好ランキングの生成モデルとランキング・パターン2010

    • Author(s)
      紙屋英彦
    • Organizer
      経済学研究科セミナー
    • Place of Presentation
      名古屋大学
    • Year and Date
      2010-06-17
    • Related Report
      2012 Final Research Report
  • [Presentation] Ranking patterns of unfolding models of codimension one

    • Author(s)
      Hidehiko Kamiya
    • Organizer
      The 2nd Institute of Mathematical Statistics Asia Pacific Rim Meeting (IMS-APRM 2012)
    • Place of Presentation
      Tsukuba International Congress Center
    • Related Report
      2012 Annual Research Report
  • [Presentation] Null robustness and marginal equivalence associated with orbital decompositions

    • Author(s)
      紙屋英彦
    • Organizer
      科研費研究集会 「数理統計学の沃野」
    • Place of Presentation
      慶應義塾大学 矢上キャンパス
    • Related Report
      2012 Annual Research Report
  • [Presentation] Rankings and hyperplane arrangements

    • Author(s)
      紙屋英彦
    • Organizer
      Forum on Probability, Statistics, Algebra and Combinatorics
    • Place of Presentation
      名古屋大学 理学部A館
    • Related Report
      2012 Annual Research Report

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

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