Analysis for contingency tables by means of algebraic technique

• Project/Area Number: 17500187
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Statistical science
• Research Institution: Kurashiki University of Science and the Arts
• Principal Investigator: NAKAGAWA Shigekazu Kurashiki University of Science and the Arts, Dept.of Computer Science and Mathematics, Professor, 産業科学技術学部, 教授 (90248203)
• Project Period (FY): 2005 – 2006
• Project Status: Completed (Fiscal Year 2006)
• Budget Amount: ¥1,200,000 (Direct Cost: ¥1,200,000); Fiscal Year 2006: ¥500,000 (Direct Cost: ¥500,000); Fiscal Year 2005: ¥700,000 (Direct Cost: ¥700,000)
• Keywords: mathematical statistics / applied mathematics / algorithm / foundation of information science

Research Abstract

The analysis with the algebraic technique which includes in Groebner basis theory as one of the recent research direction is observed in statistics, especially in contingency table analysis.
Presently, we can implement MCMC (Markov Chain Monte Carlo) on the contingency table on the computer programs.
It is designed in such a way that it can execute the p value calculation in the contingency table. Those where it is done until now are in 2 way contingency tables and no interaction model on 3 way contingency tables.
In this research, we have calculated p value for the contingency table which has the structure of especially certain kind, namely, the conditional independent model in 4 way contingency tables. Our algorithm is implemented not only on R language but also on C language. Our algorithm suggests us to apply to the graphical model on the multi way contingency tables.
Furthermore, during particular research period, we have investigated on the distribution of the sample Pearson measure of skewness and test for normality.

Research Products

• [Journal Article] Approximate cumulants of the distribution of sample generalized measure of skewness (2006)
  • Author(s): Shigekazu Nakagawa, Naoto Niki
  • Journal Title: COMPSTAT 2006, 17th Symposium of IASC-ERS, Aug. 2006.
  • Description: 「研究成果報告書概要(和文)」より
• [Journal Article] Approximate cumulants of the distribution of sample generalized measure of skewness (2006)
  • Author(s): Shigekazu Nakagawa, Naoto Niki
  • Journal Title: COMPSTAT 2006, 17th Symposium of IASC-ERS
  • Description: 「研究成果報告書概要(欧文)」より
• [Journal Article] Approximate cumulants of the distribution of sample generalized measure of skewness (2006)
  • Author(s): Shigekazu Nakagawa, Naoto Niki
  • Journal Title: Book of Abstracts, Compstat 2006 Pages: 221-221
• [Journal Article] 標本歪度・標本尖度分布の高次漸近展開における数式処理の役割 (2006)
  • Author(s): 中川重和, 仁木直人
  • Journal Title: 数式処理 13・1 Pages: 32-35
  • NAID: 10018448580
• [Journal Article] Approximate cumulants of the distribution of sample Pearson measure of skewness. (2005)
  • Author(s): NAKAGAWA, S., NIKI, N.
  • Journal Title: In : Pae, Proceedings of the Seventh Asian Symposium on Computer Mathematics(S and Park, H. (Eds.)) Pages: 203-206
  • Description: 「研究成果報告書概要(和文)」より
• [Journal Article] Approximate cumulants of the distribution of sample Pearson measure of skewness (2005)
  • Author(s): NAKAGAWA, S., NIKI, N.
  • Journal Title: In : Pae, S and Park, H. (Eds.) : Proceedings of the Seventh Asian Symposium on Computer Mathematics (ASCM 2005) 203-206
  • Description: 「研究成果報告書概要(欧文)」より
• [Journal Article] Approximate cumulants of the distribution of sample Pearson measure of skewness. (2005)
  • Author(s): NAKAGAWA, S., NIKI, N.
  • Journal Title: In : Proceedings of the Seventh Asian Symposium on Computer Mathematics (ASCM 2005)(Pae, S and Park, H.(Eds.)) Pages: 203-206
• [Journal Article] Distribution of sample Pearson measure of skewness for Pearson type populations (2005)
  • Author(s): NAKAGAWA, S., NIKI, N.
  • Journal Title: Abstrancts of 2nd German Japanese Symposium on Classification Pages: 18-18
• [Journal Article] Distribution of sample Pearson measure of skewness for Pearson type populations
  • Author(s): NAKAGAWA, S., NIKI, N.
  • Journal Title: Journal of Symbolic Computation, submitted( ) (submitted)
  • Description: 「研究成果報告書概要(欧文)」より
• [Journal Article] Computing $p$-values in the conditional independence models for a contingency table
  • Author(s): KURODA, M, HASHIGUCHI, H, NAKAGAWA, N.
  • Journal Title: COMPUTATIONAL STATISTICS ＆ DATA ANALYSIS., submitted(発表予定). (submitted)
  • Description: 「研究成果報告書概要(欧文)」より
• [Book] 統計データ科学事典 (2007)
  • Author(s): 中川重和(執筆分担)
  • Total Pages: 772
  • Publisher: 朝倉書店
  • Description: 「研究成果報告書概要(和文)」より