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Research on Shrinkage Estimator

Research Project

Project/Area Number 09640240
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 InstitutionJapan Woman's University (1998)
University of Tsukuba (1997)

Principal Investigator

SUGIURA Nariaki  Japan Women's Univ., Fac.of Sci., Professor, 理学部, 教授 (20033805)

Co-Investigator(Kenkyū-buntansha) 若林 誠一郎  筑波大学, 数学系, 教授 (10015894)
本橋 信義  筑波大学, 数学系, 教授 (70015874)
佐々木 建昭  筑波大学, 数学系, 教授 (80087436)
神田 護  筑波大学, 数学系, 教授 (80023597)
赤平 昌文  筑波大学, 数学系, 教授 (70017424)
Project Period (FY) 1997 – 1998
Project Status Completed (Fiscal Year 1998)
Budget Amount *help
¥3,200,000 (Direct Cost: ¥3,200,000)
Fiscal Year 1998: ¥900,000 (Direct Cost: ¥900,000)
Fiscal Year 1997: ¥2,300,000 (Direct Cost: ¥2,300,000)
KeywordsEstimation of covariance matrix / Non-informative prior / Test of multivariate linear hypotheses / Statistical computation / Bayes test for resticted parameters / polyhedral convex cone / 固有根に対するBayes推定 / 順序統計量 / 情報量基準 / 基準先験分布 / 線型回帰
Research Abstract

The exact risk function of the generalized Bayes estimator for bivariate normalcovariance matrix against reference prior due to Yang and Berger(1994, Ann. Statist.) is derived. It is compared with those of the Stein's minimax estimator, shrinkage estimator, Haff's estimator and orthogonally equivariant estimator by Takemura. It is found that the generalized Bayes estimator does not dominate maximum likelihood estimator at some region of the ratio of the latent root far from one and that it is very good near one.
The formula for calculating the exact power of classically famous four criteria ; likelihood ratio, maximum latent root, Hotelling's trace and Pillai's locally best invariant test for bivariate linear hypotheses are derived and the graphs of the power surfaces are demonstrated to see the global behavior. It is found that the ordering of the power : Hotelling's test<Likelihood ratio test<Pillai's test at the neighborhood of the null hypotheses and the reversed inequalities at far from the null hypotheses do not necessarily hold, though they do hold for large sample sizes.
The generalized Bayes test for loop-ordered normal means is derived which has almost the same minimum power for given non-centrality and has much larger maximum power than likelihood ratio test. It is found that the non-informative prior should be taken at the most distant corner vectors of the polyhedral convex cone formed by the alternative hypotheses. It is shown that the most distant corner vectors are made from pairs of two, each of which intersect the center of the cone with equal angle.

Report

(3 results)
  • 1998 Annual Research Report   Final Research Report Summary
  • 1997 Annual Research Report
  • Research Products

    (17 results)

All Other

All Publications (17 results)

  • [Publications] Sugiura, N.: "Reference prior Bayes estimator for fivariate normal covariance matrix." Commun.in Statist. 26(9). 2203-2221 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Sugiura, N.: "Generalized Bayes and naltiple-contrasts tests for simple loop-ordered normal means." Commun.in Statistics. 28(3)(4)(印刷中). (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] 杉浦成昭: "統計データと数理統計学のはざまに35年" 日本統計学会誌. 27. 205-220 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Sugiura, N.: "Statistical Inference and Related Topics" eds. S.E.Ahmed, M.Ahsanullch XB.K.Sinha, Nova Sci.Pnf.(in press), (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] 杉浦成昭: "保健統計学(多変量解析第2章)" 培風館, 28 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] N.Sugiura.: "Reference prior Bayes estimator for bivariate normal covariance matrix" Commun.in Statist.26(9). 2203-2221 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] N.Sugiura.: "Generalized Bayes and multiple-contrasts tests for simple loop-ordered normal means with risk comparison" Commun.in Statist.28(3 & 4) (in press). (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] N.Sugiura.: "35 years in between statistical data and mathematical statistics (in Japanese)" J.Jap.Stat.Soc.27. 205-220 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] N.Sugiura: Statistical Inference and Related topics eds.S.E.Ahmed, M.Ahsanullah, & B.K.Sinha. Nova Sci.Pub. (in press), (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] N.Sugiura: "Chapter 2 Multivariate Analysis"in Health Statistics. Baifu-kan Pub., 28 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Sugiura,N.: "Reference prior Bayes estimator for bivariate normal covariance matrix." Commun.in Statist.26(9). 2203-2221 (1997)

    • Related Report
      1998 Annual Research Report
  • [Publications] Sugiura,N.: "Generalized Bayes and multiple contrasts tests for simple loop-ordered normal means." Commun.in Statist.28(3,4)(印刷中). (1999)

    • Related Report
      1998 Annual Research Report
  • [Publications] 杉浦成昭: "統計データと数理統計学のはざまに35年" 日本統計学会誌. 27巻3号. 205-220 (1997)

    • Related Report
      1998 Annual Research Report
  • [Publications] Sugiura,N.: "Statistical Inference and Related Topics" eds.S.E.Ahmed. M.Ahsarulluh & B.K.Sinka Nova Sci.Pub.(印刷中), (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] 杉浦成昭: "保健統計学(多変量解析第2章)" 培風館, 28 (1997)

    • Related Report
      1998 Annual Research Report
  • [Publications] Sugiura N. and lohibayashi,H.: "Reference prior Bayes estimator for bivariate normal yaria matrix with risk comgarison" Communications in Statistics. 26(9). 2203-2221 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] 杉浦成昭: "統計データと教理統計学のはざまに35年" 日本統計学会誌. 27(3). 205-220 (1997)

    • Related Report
      1997 Annual Research Report

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Published: 1997-04-01   Modified: 2016-04-21  

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