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A new development of a conditional test (specially its sequential version) for contingency tables and the related problems

Research Project

Project/Area Number 13640121
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 InstitutionKyushu Institute of Design

Principal Investigator

SAKATA Toshio  Kyusyu Institute of Design, Industrial Design, Professor, 芸術工学部, 教授 (20117352)

Co-Investigator(Kenkyū-buntansha) SASABUCHI Syouichi  Kyusyu Institute of Design, Common technical course, Professor, 芸術工学部, 教授 (20128028)
NOMAKUCHI Kentaro  Kochi University, Mathematics, Professor, 理学部, 教授 (60124806)
SAWAE Ryuichi  Okayama University of Science, Applied Mathematics, Associate Professor, 理学部, 助教授 (20226062)
XU YU Jeferry  Chinese University of Hong Kong, System Engineering and Management Engineering, Associate Professor
Project Period (FY) 2001 – 2002
Project Status Completed (Fiscal Year 2002)
Budget Amount *help
¥2,600,000 (Direct Cost: ¥2,600,000)
Fiscal Year 2002: ¥900,000 (Direct Cost: ¥900,000)
Fiscal Year 2001: ¥1,700,000 (Direct Cost: ¥1,700,000)
KeywordsContingency tables / Conditional exact test / Creation Operator / Size of the test / Power of the sequential test / Quantum MCMC on the set of contingency tables / Three way tables / MCMC in constrained inference / 条検付正確検定 / クリエーシヨン作用素 / 不等式制約下の相関行列のMCMC推定
Research Abstract

The aim of this research was to develop a theory of the sequential conditional test for contingency tables. The sequential conditional test was constructed via the creation operator for A-hypergeometric partial differential equation systems. This idea was motivated by the works of Takayama et al. for integer programming problems. The implementation problem of the test and its power performance for the two way tables was examined in the year 2001. It was shown that for moderate size of two way tables the sequential test performs well on PC. The result was published in the several international conference, ICPR in Prague and 53^<rd> ISI in Seoul and ICNCB in Osaka. The second year 2002, we attacked the construction of the sequential conditional test for three way tables of type 3x3x3. The performance was good. The result was published in the international conference SCI2002, in Florida. Then our sequential test is based on the minimal Markov basis developed by Takemura and Aoki. Therefor … More e we are now pursuing the algebraic theory of constructing minimal Markov basis for three way tables initiated by Takemura and Aoki. The recent development of the algebraic theory of MCMC on the set of contingency tables was discussed in our special lecture of 16^<th> annual meeting of the Japanese computational statistical society. Further Sakata and Sawae considered the quantum version of Metropolis walk on the set of contingency tables. This was published in Journal of quantum chemistry. Further Sakata, Sawae and Nomakuchi considered the Gibbs walks on the set of correlation matrix for the constraind hypothesis of components correlation. This was published the book of Advance in Statistics, Combinatrics and related fields edited by Chandra Gulti et.al. Sakata and Jeffery Xu Yu published in Wireless Network about the estimating problem of access frequency from the request. Sasabuchi published two paper for the worldwide famous journal about the restricted inference. Nomakuchi published three papers about restricted inference. Jeferry Xu Yu published many papers and gave talks at many international conferences about Data Mining. As a result our project produced several refereed papers successfully. Less

Report

(3 results)
  • 2002 Annual Research Report   Final Research Report Summary
  • 2001 Annual Research Report
  • Research Products

    (45 results)

All Other

All Publications (45 results)

  • [Publications] Sakata, T., Sawae, R.: "計算機統計と数学の連携(分割表の解析の最近の話題から)"日本計算機統計学会16回大会論文集(特別講演). 92-99 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Sakata, T., Sawae, R.: "A study of the sequential ; conditional test for 3x3x3 contingency tables"The proceeding of the 6-th World Multiconference on Sytemics, Cybernetics and Informatics. Vol 17. 406-410 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Sawae, R., Sakata, T., et al.: "Quantum Random Walks on the set of Contingency Tables"International Journal of Quantum Chemistry. Vol.90. 1321-1325 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Sakata, T., Sawae, R., Nomakuchi, K.: "Maximum likelihood estimation of correlation matrix under inequality constraints using Gibbs sampling"Advances in Statistics, Combinatorics and Related Areas, World Scientific Chandra Gulati, Yan-Xia Lin, Satya Misha, John Rayner eds.. 258-266 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Sakata, T., Sawae, R.: "A study of the sequential conditional test for contingency tables"Journal of the Japanese Society of Computational Statistics. Vol15(掲載予定). (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Sakata, T., Xu Yu J.: "Statistical Estimation of Access Frequencies: Problems, Solutions and Consistencies"Wireless Networks. (掲載予定). (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Sasabuchi, S., Miura T., Oda, H.: "Estimation and Test of Several Multivariate Normal Means Under an Order Restriction when the Dimension is Larger than Tow"Journal of Statistical Computation and Simulation. (掲載予定). (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Sasabuchi, S., Tanaka K., Tsukamoto, T.: "Testing homogeneity of multivariate normal mean vectors under an order restriction when covariance matrices are common but unknown"The Annals of Statistics. (掲載予定). (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Kikuchi, Y., Nomakuchi, K.: "Two modifications of hidden Markov model anti their comparison"Mem.Fac.Sci.Kochi Univ.(Math.). Vol.23. 99-127 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Nomakuchi, K.: "A Monotonicity of Moments concerned with order restricted statistical inference"Ann.Inst.Statist.Math.. Vol.54. 621-625 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Nomakuchi, K.: "On the algorithm of Dykstra in a quadratic programming problem on a closed convex cone"Mem.Fac.Sci.Kochi Univ.(Math.). Vol 24(掲載予定). (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Jefferey Xu Yu, Michael.K.Ng, J.Z.Huang: "Patterns Discovery Based on Times-Series Decomposition"Springer Lecture Note in Computer Science. Vol 2035. 336-347 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] G.P.C.Fung, J.Xu Yu, H.Lu: "Discriminative Category Matching : Efficient Text Classification for Huge Document Collections"Proceedings of the Second IEEE International Conference on Data Mining. (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Fung G.P.C., Xu Yu J, Lam, W.: "New Sensitive Stock Trend Prediction"Springer-Verlag L.N.in Computer Science. Vol 2336. 481-494 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Sakata,T., and Sawae,R.: "A study of the sequential; conditional test for 3x3x3 contingency tables"The proceeding of the 6-th World Multiconference on Systemics, Cybernetics and Informatics. 17. 406-410 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Sawae,R., Sakata,T., et.al.: "Quantum Random Walks on the set of Contingency Tables"International Journal of Quantum Chemistry. 90. 1321-1325 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Sakata,T., and Sawae,R.: "A study of the sequential conditional test for contingency tables"Journal of the Japanese Society of Computational Statistics. 15(to be published). (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Sakata,T., and Xu Yu J.: "Statistical Estimation of Access Frequencies: Problems, Solutions and Consistencies"Wireless Network. (to be published). (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Sasabuchi,S., Miura,T., and Oda,H.: "Estimation and Test of Several Multivariate Normal Means Under an Order Restriction when the Dimension is Larger than Two"Journal of Statistical Computation and Simulation. (Accepted). (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Sasabuchi,S., Tanaka,K., and Tsukamoto,T.: "Testing homogeneity of multivariate normal mean vectors under an order restriction when the covariance matrices are common but unknown"The Annals of Statistics. (to be published). (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Kikuchi,Y., and Nomakuchi,K.: "Two modifications of hidden Markov model and their comparison"Mem Fac. Sci. Kochi Univ. (Math.). 23. 99-127 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Nomakuchi,K.: "A Monotonicity of Moments concerned with order restricted statistical inference"Ann. Inst. Statist. Math.. 54. 621-625 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Nomakuchi,K.: "On the algorithm of Dykstra in a quadratic programming problem on a closed convex cone"Mem. Fac. Sci. Kochi. Univ. (Math.). 24(to be published). (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Jefferey Xu Yu and Michael.K.Ng and J.Z.Huang.: "Patterns Discovery Based on Times-Series Decomposition"Springer Lecture Note in Computer Science. 2035. 336-347 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] G.P.C.Fung., J.Xu Yu and H.Lu.: "Discriminative Category Matching: Efficient Text Classification for Huge Document Collections"Proceeding of the Second IEEE International Conference on Data Mining. (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Fung G.P.C. and Xu Yu J. and Lam,W.: "New Sensitive Stock Trend Prediction"Springer-Verlag L.N. in Computer Science. 2336. 484-494 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Sakata,T., Sawae,R., and Nomakuchi,K., Chandra Gulati(eds.), Yan-Xia Lin(eds.), Satya Misha(eds.), John Rayner(eds.): "Maximum likelihood estimation of correlation matrix under inequality constraints using Gibbs sampling, Advances in Statistics, Combinatorics and Related Areas"World Science Chandra Gulati. 258-266 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Sakata, T., Sawae, R.: "計算機統計と数学の連携(分割表の解析の最近の話題から)"日本計算機統計学会16回大会論文集(特別講演). 92-99 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] Sakata, T., Sawae, R.: "A study of the sequential ; conditional test for 3x3x3 contingency tables"The Proceeding of the 6-th World Multiconference on Sytemics, Cybernetics and Informatics. Vol17. 406-410 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] Sawae, R, Sakata, T, et al.: "Quantum Random Walks on the set of Contingency Tables"International Journal of Quantum Chemistry. Vol.90. 1321-1325 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] Sakata, T., Sawae, R., Nomakuchi K.: "Maximum likelihood estimation of correlation matrix under inequality constraints using Gibbs sampling"Advances in Statistics, Combinatorics and Related Areas, World Scientific Chandra Gulati, Yan-Xia Lin, Satya Misha, John Rayner eds.. 258-266 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] Sakata, T., Sawae R.: "A study of the sequential conditional test for contingency tables"Journal of the Japanese Society of Computational Statistics. Vol15(掲載予定). (2003)

    • Related Report
      2002 Annual Research Report
  • [Publications] Sakata, T., Xy Yu J.: "Statistical Estimation of Access Frequencies : Problems, Solutions and Consistencies"Wireless Networks. (掲載予定). (2003)

    • Related Report
      2002 Annual Research Report
  • [Publications] Sasabuchi, S., Miura T., Oda H.: "Estimation and Test of Several Multivariate Normal Means Under an Order Restriction when the Dimension is Larger than Two"Journal of Statistical Computation and Simulation. (掲載予定). (2003)

    • Related Report
      2002 Annual Research Report
  • [Publications] Sasabuchi, S., Tahaka K., Tsukamoto, T.: "Testing homogeneity of multivariate normal mean vectors under an order restriction when the covariance matrices are common but unknown"The Annals of Statistics. (掲載予定). (2003)

    • Related Report
      2002 Annual Research Report
  • [Publications] Kikuchi, Y., Nomakuchi K.: "Two modifications of hidden Markov model and their comparison"Mem. Fac. Sci. Kochi Univ. (Math.). Vol.23. 99-127 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] Nomakuchi, K.: "A Monotonicity of Moments concerned with order restricted statistical inference"Ann. Inst. Statist. Math.. Vol.54. 621-625 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] Nomakuchi, K.: "On the algorithm of Dykstra in a quadratic programming problem on a closed convex cone"Mem. Fac. Sci. Kochi Univ. (Math.). Vol24(掲載予定). (2003)

    • Related Report
      2002 Annual Research Report
  • [Publications] Fung G.P.C., Xu Yu J, Lam, W.: "New Sensitive Stock Trend Prediction"Springer-Verlag L.N. in Computer Science. Vol2336. 481-494 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] Sakata, T.Sawae, R.Krournov, R.: "Applications of Groebner basis to analysis of contingency tables and integer programming"Proceedings C.D. of 16-th International Conference on Product Research. Section E-7.3-9 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] Sakata.T, Sawae, R.: "Hypergeometric Systems, Weyl Algebra, Creation Operator, and Sequentila Inference of Contingency Tables"Bulletine of the Institute of the International Statistical Institute, 53^<rd> Session, Contributed papers. 1巻. 383-384 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] Sakata, T., Sawae, R.: "A study of the sequential conditional test for contingency tables"Proceedings of the International Conference on New Trends in Computational Statistics with Biomedical Applications. 377-382 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] Sawae, R., Sakata, T., Takarabe, K., Tei, M.: "Quantum random walks on the set of contingency tables"第5回量子情報技術研究会資料集. 105-110 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] Sakata, T., Sawae, R., Nomakuchi, K.: "Maximum Likelihood Estimation of Correlation Matrix under Inequality Constraints using Gibbs Sampling"Preproceedling Book of International Conference on Statistics, Combinatrics and related Area. 8 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] Kikuchi, Y., Nomakuchi, K: "Two Modifications of Hidden Markov Model and Their Model Comparison"Mem. Fac. Sci. Kochi University(Mathematics). 23巻. 99-127 (2002)

    • Related Report
      2001 Annual Research Report

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Published: 2001-04-01   Modified: 2016-04-21  

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