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New Multivariate-Distribution Estimators in view of Decision Theory

Research Project

Project/Area Number 15530142
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Economic statistics
Research InstitutionSHINSHU UNIVERSITY

Principal Investigator

SHEENA Yo  SHINSHU UNIVERSITY, Department of Economics, Professor, 経済学部, 教授 (80242709)

Project Period (FY) 2003 – 2006
Project Status Completed (Fiscal Year 2006)
Budget Amount *help
¥2,100,000 (Direct Cost: ¥2,100,000)
Fiscal Year 2006: ¥500,000 (Direct Cost: ¥500,000)
Fiscal Year 2005: ¥600,000 (Direct Cost: ¥600,000)
Fiscal Year 2004: ¥500,000 (Direct Cost: ¥500,000)
Fiscal Year 2003: ¥500,000 (Direct Cost: ¥500,000)
Keywordsunbiasedness / Wishart distribution / orthogonally equivariant estimator / minimax / eigenvalues / covariance matrix / asymptotic distribution / Zonal Polynomials / 多変量正規分布 / 漸近展開 / 多変量解析 / 標本固有値 / 損失関数 / シュタイン / ウィッシャート分布 / 楕円分布 / 不変検定 / 検定力の単調性 / 検定の不偏性 / 不変推定量
Research Abstract

1. We gained the following result on orthogonally equivariant estimators for a non-negative definite random matrix whose density is expanded as a series of zonal polynomials with a non-negative definite matrix parameter.
1) With respect to Stein's loss function, non-order-preserving estimators for the matrix parameter are conjectured to be inadmissible. We proved this for 2-dimensional case.
2) We found an integral inequality on zonal polynomials on the group of orthogonal matrices is a sufficient condition for the above conjecture.
2. Through joint research with Professor Takemura (Tokyo University), we found the following result on an asymptotics when the population eigenvalues of Wishart matrix is infinitely dispersed.
1) Based on the asymptotic distributions which were previously gained, we derived higher-order expansions for those distributions.
2) We derived using the expansions a necessary condition for an estimator of the covariance matrix to be tail-minimax. We applied this result to Stein and Haff estimators and found neither of them is minimax.
3. We considered one-sided test for the null hypothesis that the covariance matrix is equal to a given matrix. The unbiasedness for an invariant test which has a monotone critical region with respect to the eigenvalues was already proved in 60's. We found an alternative proof for the result.

Report

(5 results)
  • 2006 Annual Research Report   Final Research Report Summary
  • 2005 Annual Research Report
  • 2004 Annual Research Report
  • 2003 Annual Research Report
  • Research Products

    (7 results)

All 2007 2005

All Journal Article (7 results)

  • [Journal Article] An asymptotic expansion of Wishart distribution when the population eigenvalues are infinitely dispersed.2007

    • Author(s)
      Yo Sheena
    • Journal Title

      Statistical Methodology 第4巻

      Pages: 158-184

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] An asymptotic expansion of Wishart distribution when the population eigenvalues are infinitely dispersed.2007

    • Author(s)
      Yo Sheena
    • Journal Title

      Statistical Methodology Vol.4

      Pages: 158-184

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] An asymptotic expansion of Wishart distribution when the population eigenvalues are infinitely dispersed.2007

    • Author(s)
      Yo Sheena, Akimichi Takemura
    • Journal Title

      Statistical Methodology 4巻

      Pages: 158-184

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Order-preserving estimators and an inequality on the integration of zonal polynomials2005

    • Author(s)
      Yo Sheena
    • Journal Title

      Communications in Statistics-Theory and Methods 34巻7号

      Pages: 1503-1516

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Order-preserving estimators and an inequality on the integration of zonal polynomials.2005

    • Author(s)
      Yo Sheena
    • Journal Title

      Communications in Statistics-Theory and Method Vol.34

      Pages: 1503-1516

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Order-Preserving estimators and an inequality on the integration of zonal polynomial2005

    • Author(s)
      Yo Sheena
    • Journal Title

      Communications in Statistics -Theory and Methods- 34/7(印刷中)

    • Related Report
      2004 Annual Research Report
  • [Journal Article] On unbiasedness of invariant tests of sphericity2005

    • Author(s)
      Yo Sheena
    • Journal Title

      Journal of Multivariate Analysis (発表予定)

    • Related Report
      2004 Annual Research Report

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Published: 2003-04-01   Modified: 2016-04-21  

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