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

Distribution problem of discriminant and regression analysis for directional data

Research Project

Project/Area Number 63530009
Research Category

Grant-in-Aid for General Scientific Research (C)

Allocation TypeSingle-year Grants
Research Field 統計学
Research InstitutionHITOTSUBASHI UNIVERSITY

Principal Investigator

HAYAKAWA Takesi  Hitotsubashi University, Department of Economics, Professor, 経済学部, 教授 (00000183)

Co-Investigator(Kenkyū-buntansha) HAYAKAWA Takesi  Hitotsubashi University, Department of Economics Professor (00000183)
Project Period (FY) 1988 – 1989
Project Status Completed (Fiscal Year 1989)
Budget Amount *help
¥1,900,000 (Direct Cost: ¥1,900,000)
Fiscal Year 1989: ¥600,000 (Direct Cost: ¥600,000)
Fiscal Year 1988: ¥1,300,000 (Direct Cost: ¥1,300,000)
KeywordsLangevin population / Likelihood ratio criterion / Wald statistic / Watson statistic / Discriminant analysis / Misclassification / Plug-in statistic / Rao statistic / Langerin分布 / Wald統計量 / Plug-In統計量 / Rao統計量 / 誤判別確率 / 検出力 / Langevin分布 / 改良Wald統計量 / Elliptical母集団 / F-集団 / 固有値
Research Abstract

This research studied the following problems. (1) Tests of parameters (mean direction and concentration parameter) of Langevin population on a sphere. Test statistics (Likelihood ratio criterion, Watson statistic, Wald statistic, Rao statistic etc.) are proposed and asymptotic expansions of the distributions of these are obtained. The simulation experiments show that the asymptotic expansions give good agreements with simulation results. (2) The discriminant functions (Plug-In statistic and Likelihood ratio criterion) for two Langevin populations are proposed. The comparison of these in done from theoretical and simulational points of view. (3) The survey was done for the recent development of zonal polynomials and invariant polynomials which are fundamental ones for the study, of the distributional problems in multivariate analysis.

Report

(3 results)
  • 1989 Annual Research Report   Final Research Report Summary
  • 1988 Annual Research Report
  • Research Products

    (15 results)

All Other

All Publications (15 results)

  • [Publications] T.Hayakawa: "On the tests for the mean direction of the langevin distribution" Ann.Inst.Statist.Math.

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1989 Final Research Report Summary
  • [Publications] T.Hayakawa: "Invariant polynomials and related tests" Amerrican Jour.Math.and Management Sciences.

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1989 Final Research Report Summary
  • [Publications] T.Hayakawa: "On some tests for parameters of Langevin population"

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1989 Final Research Report Summary
  • [Publications] T.Hayakawa: "Discriminant analysis for langevin population"

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1989 Final Research Report Summary
  • [Publications] T.Hayakawa: "On the distributions of the functions of the F-matrix under an elliptical population" Pour.Statist.Plann.and Inf.21. 41-52 (1989)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1989 Final Research Report Summary
  • [Publications] T.Hayakawa: "On the tests for the mean direction of the Langevin distribution." Ann. Inst. Statist. Math.

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1989 Final Research Report Summary
  • [Publications] T.Hayakawa: "Invariant polynomials and related tests." American Jour. Math. Manag. Sciences.

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1989 Final Research Report Summary
  • [Publications] T.Hayakawa: "On some tests for parameters of Langevin population."

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1989 Final Research Report Summary
  • [Publications] T.Hayakawa: "Discriminant analysis for Langevin population."

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1989 Final Research Report Summary
  • [Publications] T.Hayakawa: "On the distributions of the functions of the F-matrix under an elliptical population." Jour. Statist. Plann. and Inf.21. 41-52 (1989)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1989 Final Research Report Summary
  • [Publications] T.Hayakawa: "On some tests for parameters of Langevin population"

    • Related Report
      1989 Annual Research Report
  • [Publications] T.Hayakawa: "Discriminant analysis for Langevin population"

    • Related Report
      1989 Annual Research Report
  • [Publications] T.Hayakawa: Ann Inst.Statist.Math.

    • Related Report
      1988 Annual Research Report
  • [Publications] T.Hayakawa: American Jour.Math.and Management Sciences.

    • Related Report
      1988 Annual Research Report
  • [Publications] T.Hayakawa: Jour.Statist.Plann.and Inf.21. 41-52 (1989)

    • Related Report
      1988 Annual Research Report

URL: 

Published: 1988-04-01   Modified: 2016-04-21  

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi