• Search Research Projects
  • Search Researchers
  • How to Use
  1. Back to previous page

Evaluation of Predictive Distributions based on Information and Entropy

Research Project

Project/Area Number 08454043
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section一般
Research Field General mathematics (including Probability theory/Statistical mathematics)
Research InstitutionKYUSYU UNIVERSITY

Principal Investigator

KONISHI Sadanori  Kyushu Univ.Graduate School of Math.Professor, 大学院・数理学研究科, 教授 (40090550)

Co-Investigator(Kenkyū-buntansha) FUEDA Kaoru  Kyushu Univ.Graduate School of Math.Kyushu University Research Associate, 大学院・数理学研究科, 助手 (50253399)
NAKAO Mituhiro  Kyushu Univ.Graduate School of Math.Kyushu University Professor, 大学院・数理学研究科, 教授 (10136418)
TANAKA Shun-ichi  Kyushu Univ.Graduate School of Math.Kyushu University Professor, 大学院・数理学研究科, 教授 (00028127)
YANAGAWA Takashi  Kyushu Univ.Graduate School of Math.Kyushu University Professor, 大学院・数理学研究科, 教授 (80029488)
Project Period (FY) 1996
Project Status Completed (Fiscal Year 1996)
Budget Amount *help
¥2,400,000 (Direct Cost: ¥2,400,000)
Fiscal Year 1996: ¥2,400,000 (Direct Cost: ¥2,400,000)
KeywordsInformation Criteria / Bootstrap Methods / Nonlinear Models / Equivalence tests / Elliptic Boundary Value Problems / Numerical Solution with Guaranteed Error Bounds / Object-Intensive Language / Nonparametric Tests
Research Abstract

The purpose of the research is to investigate the problem of evaluating the goodness of statistical models from an information-theoretic point of view. The following are the main results obtained through this research project extending over 1996.
1. Information criteria were proposed for evaluating statistical models constructed by various estimation procedures when the specified family of probability distributions does not contain the distribution generating the data. The proposed criteria are applied to the evaluation of models estimated by maximum likelihood, robust, penalized likelihood, Bays procedures, etc. In regard to computer-intensive methods the theoretical and practical aspects of the use of the bootstrap were investigated in model evaluation problems. 2. Equivalence tests for binary data with pair-matched design in clinical trials were explored. Eight tests were investigated altogether including those tests constructed by the GSK method, the tests which use estimated null variances among others. 3. A numerical enclosure method with guaranteed L^* error bounds for the solution of nonlinear elliptic problems of second order were investigated. Using an a posteriori error estimates for the approximate solution of the problem with higher order C^0-finite element, it was shown that we can obtain the guaranteed L^* error boundswith high accuracy. 4. The verification procedure were extended to nondifferentiable nonlinear elliptic problem related to MHD equilibra, and a computing algorithm which automatically encloses the solution with guaranteed error bounds was constructed. 5. Unified construction procedure of class of rank tests were investigated and the asymptotic normality was proved for test statistics for the two-sample problem derived by the convex sum distance.

Report

(2 results)
  • 1996 Annual Research Report   Final Research Report Summary
  • Research Products

    (33 results)

All Other

All Publications (33 results)

  • [Publications] Ichikawa,M.: "Bootstrap tests for the goodness of fit in factor analysis." To appear in special issue of Covariance Structure Analysis Behaviormetrika. (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] Konishi,S.: "Generalized information criteria in model selection." Biometrika. 83. 875-890 (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] Zhao,Y.: "Effect of a shrinkage estimator on the linear discriminant function." American Journal of Mathematicaland Management Sciences. 16. 109-130 (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] Zhao,Y.: "Limit distributions of multivariate kurtosis and moments under Watson rotational symmetric distributions." Statistics and Probability Letters in press.

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] Morikawa T.: "Equivalence tests for pair-matched binary data" Bull.of Informatics and Cybernetics. 28. 31-45 (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] Endoh,A.: "A proposal for testing equivalence or more than equivalence for pair-matched case in comparative clinical trials" Japanese J of Applied Statistics. 24. 59-73 (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] Minamoto,T.: "Numerical verifications of solutions for nonlinear parabolic equations in one-space dimensional case" To appear in Reliable Computing. (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] Tsuchiya,T.: "Numerical verification of solutions of parametrized nonlinear boundary value problems with turning points" To appear in Japan Journal of Industrial and Applied Mathematics.(1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] Watanabe,Y.: "Verified computation of solutions for nondifferentiable elliptic equations related to MHD equilibria." Nonlinear Analysis,Theory,Methods & Applications. 28. 577-587 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] Nakao,M.T.: "Guaranteed error bounds for finite element solutions of the Stokes problem." Scientific Computing and Validated Numerics (G.Alefeld et al.eds.), Akademie Verlag,Berlin. 258-264 (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] Fueda,K.: "The limiting normality of the test statistic for the two-sample problem induced by a convex sum distance." Annals of the Institute of Statistical Mathematics. 48. 337-347 (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] Ichikawa, M: "Bootstrap tests for the goodness of fit in factor analysis." To appear in special issue of Covariance Structure Analysis Behaviometrika. Vol.24. (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] Konishi, S: "Generalized information criteria in model selection." Biometrika. Vol.83, No.4. 875-890 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] Zhao, Y.: "Effect of a shrinkage estimator on the linear discriminant function." American Journal of Mathematicaland Management Sciences. 109-130 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] Zhao, Y.: "Limit distributions of multivariate kurtosis and moments under Watson rotational symmetric distributions." Statistics and Probability Letters. (in press). (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] Morikawa T.Yoshimura I.: "Equivalence tests for pair-matched binary data" Bull.of Informatics and Cybernetics. Vol.28, No.1. 31-45 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] Endoh, A.: "A proposal for testing equivalence or more than equivalence for pair-matched case in comparative clinical trials" Japanese J of Applied Statistics. Vol.24. 59-73 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] Minamoto, T.: "Numerical verifications of solutions for nonlinear parabolic equations in one-space dimensional case" To appear in Reliable Computing. Vol.3. (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] Tsuchiya, T.: "Numerical verification of solutions of parametrized nonlinear boundary value problems with turning points" To appear in Japan Journal of Industrial and Applied Mathematics.

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] Watanabe, Y.: "Verified computation of solutions for nondifferentiable elliptic equations related to MHD equilibria" Nonlinear Analysis, Theory, Methods & Applications. 28. 577-587 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] Nakao, M.T.: "Guaranteed error bounds for finite element solutions of the Stokes problem." Scientific Computing and Validated Numerics (G.Alefeld et al.eds.), Akademie Verlag, Berlin. 258-264 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] Fueda, K.: "The limiting normality of the test statistics for the two-sample problem induced by a convex sum distance." Annals of the institute of statistical mathematics. Vol.48, No.2. 337-347 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] Minamoto,T.: "Numerical verification of solutions for nonlinear parabolic equations in one-space dimensional case" Reliable Computing. (to appear). (1997)

    • Related Report
      1996 Annual Research Report
  • [Publications] Tsuchiya,T.: "Numerical verifications of solutions of parametrized nonlinear boundary value problems with turning points" in Japan Journal of Industrial and Applied Mathematics.(to appear). (1997)

    • Related Report
      1996 Annual Research Report
  • [Publications] Watanabe,Y.: "Verified computation of solutions for nondifferentiable elliptic equations related to MHD equilibria." Nonlinear Analysis,Theory,Methods & Applications. 28. 577-587 (1997)

    • Related Report
      1996 Annual Research Report
  • [Publications] Nakao,M.T.: "Guaranteed error bounds for finite element solutions of the Stokes problem." Scientific Computing and Validated Numerics. 258-264 (1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] Fueda,K.: "The limiting normality of the test statistic for the two-sample problem induced by a convex sum distance." Annals of the Institute of Statistical Mathematics. 48・2. 337-347 (1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] Ichikawa,M.: "Bootstrap tests for the goodness of fit in factor analysis." To appear in special issue of Covariance Structure Analysis Behavior,etrika. (1997)

    • Related Report
      1996 Annual Research Report
  • [Publications] Konishi,S.: "Generalized information criteria in model selection." Biometrika. 83・4. 875-890 (1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] Zhao,Y.: "Effect of a shrinkage estimator on the linear discriminant function." American Journal of Mathematicaland Management Sciences. 16・2. 109-130 (1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] Zhao,Y.: "Limit distributions of multivariate kurtosis and moments under Watson rotational symmetric distributions." Statistics and Probability Letters. (in press). (1997)

    • Related Report
      1996 Annual Research Report
  • [Publications] Morikawa,T.: "Equivalence tests for pair-matched binary data" Bull.of Informatics and Cybernetics. 28・1. 31-45 (1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] Endoh,A.: "A proposal for testing equivalence or more than equivalence for pair-matched case in comparative clinical trials" Japanese J of Applied Statistics. 24. 59-73 (1996)

    • Related Report
      1996 Annual Research Report

URL: 

Published: 1996-04-01   Modified: 2016-04-21  

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi