Modeling and orthogonal decompositions of symmetry for contingency tables

2010 Fiscal Year Final Research Report

• Project/Area Number: 21740084
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Single-year Grants
• Research Field: General mathematics (including Probability theory/Statistical mathematics)
• Research Institution: Tokyo University of Science
• Principal Investigator: TAHATA Kouji Tokyo University of Science, 理工学部・情報科学科, 助教 (30453814)
• Project Period (FY): 2009 – 2010
• Keywords: 統計数学 / 分割表解析

Research Abstract

In this research, for the analysis of square contingency tables, we proposed some symmetry models. Also, we gave the orthogonal decompositions of model into some models that have weaker restrictions than the model. These results will work well for the analysis of square contingency tables.

Research Products

• [Journal Article] Risk of estimators for point symmetry and double symmetry models for square contingency tables. (2011)
  • Author(s): Kouji Tahata, Takahiro Inoue, Sadao Tomizawa.
  • Journal Title: nternational Journal of Pure and Applied Mathematics. Vol.66 Pages: 25-32
  • Peer Reviewed
• [Journal Article] Double linear diagonals-parameter symmetry and decomposition of double symmetry for square tables. (2010)
  • Author(s): Kouji Tahata, Sadao Tomizawa.
  • Journal Title: Statistical Methods and Applications. Vol.19 Pages: 307-318
  • Peer Reviewed
• [Journal Article] On test of marginalpoint-symmetry in multi-way tables. (2010)
  • Author(s): Kouji Tahata, Hiroki Tokuno, Sadao Tomizawa.
  • Journal Title: Advances and Applications in Statistical Sciences Vol.3 Pages: 1-12
  • Peer Reviewed
• [Journal Article] Measures of departurefrom Bradley-Terry model for squaretables : application to baseball. (2010)
  • Author(s): Kouji Tahata, Akihito Tomita, Sadao Tomizawa.
  • Journal Title: International Journal of Sports Science and Engineering. Vol.4 Pages: 195-208
  • Peer Reviewed
• [Journal Article] Decomposition of diagonals-parameter symmetry modeland orthogonality of its test statisticfor square contingency tables with ordered categories. (2009)
  • Author(s): Kouji Tahata, Sadao Tomizawa.
  • Journal Title: Journal of Statistical Theory and Applications. Vol.8 Pages: 406-415
  • Peer Reviewed
• [Journal Article] A measure of departure from average symmetry for square contingency tables with ordered categories. (2009)
  • Author(s): Kouji Tahata, Kouji Yamamoto, Noriyuki Nagatani, Sadao Tomizawa.
  • Journal Title: Austrian Journal of Statistics. Vol.38 Pages: 101-108
  • Peer Reviewed
• [Journal Article] Decomposition of symmetry using tworatios-parameter symmetry model and orthogonality for square contingency tables. (2009)
  • Author(s): Kouji Tahata, Sadao Tomizawa.
  • Journal Title: Journal of Statistics: Advances in Theory and Applications. Vol.1 Pages: 19-33
  • Peer Reviewed
• [Journal Article] Normal distribution type symmetry model for square contingency tables with ordered categories. (2009)
  • Author(s): Kouji Tahata, Kouji Yamamoto, Sadao Tomizawa.
  • Journal Title: Open Statistics and Probability Journal. Vol.1 Pages: 32-37
  • Peer Reviewed
• [Presentation] 正方分割表における二重対称性の分解について (2011)
  • Author(s): 田畑耕治、富澤貞男
  • Organizer: 日本数学会
  • Place of Presentation: 早稲田大学
  • Year and Date: 2011-03-21
• [Presentation] 順序カテゴリをもつ正方分割表における対称性の分解について (2010)
  • Author(s): 田畑耕治、富澤貞男
  • Organizer: 日本数学会
  • Place of Presentation: 名古屋大学
  • Year and Date: 2010-09-24
• [Presentation] 分割表における準対称性からの隔たりを測る距離尺度 (2010)
  • Author(s): 田畑耕治、冨田聡人、富澤貞男
  • Organizer: 統計関連学会連合
  • Place of Presentation: 早稲田大学
  • Year and Date: 2010-09-08
• [Presentation] Bradley-Terry モデルからの隔たりを測る距離尺度 (2010)
  • Author(s): 田畑耕治、冨田聡人、富澤貞男
  • Organizer: 応用統計学会
  • Place of Presentation: 統計数理研究所
  • Year and Date: 2010-05-20
• [Presentation] 対称性と非対称性のモデルに基づく分割表解析 (2009)
  • Author(s): 田畑耕治
  • Organizer: 日本数学会
  • Place of Presentation: 大阪大学
  • Year and Date: 2009-09-26
• [Presentation] 多元分割表における点対称モデルの分解 (2009)
  • Author(s): 田畑耕治、富澤貞男
  • Organizer: 統計関連学会連合
  • Place of Presentation: 同志社大学
  • Year and Date: 2009-09-07
• [Presentation] 正方分割表における非対称性を測る尺度とその応用 (2009)
  • Author(s): 田畑耕治、山田章史、山本紘司、富澤貞男
  • Organizer: 応用統計学会
  • Place of Presentation: 統計数理研究所
  • Year and Date: 2009-08-01
• [Presentation] 分割表における点対称性からの隔たりを測る尺度 (2009)
  • Author(s): 田畑耕治、山本紘司、富澤貞男
  • Organizer: 日本計算機統計学会
  • Place of Presentation: 福岡女子大学
  • Year and Date: 2009-05-17
• [Remarks] ホームページ等
  • URL: http://www.sut.ac.jp/fac_grad/p/index.php?A15578