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Stein phenomena and further development on shrinkage methods

Research Project

Project/Area Number 13680369
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Statistical science
Research InstitutionJapan Women's University (2003-2004)
Chiba University (2001-2002)

Principal Investigator

KONNO Yoshihiko  Japan Women's University, Faculty of Science, Associate Professor, 理学部, 助教授 (00205577)

Co-Investigator(Kenkyū-buntansha) SHIRAISHI Taka-aki  Yokohama city University, Department of Mathematical Science, Professor, 大学院・総合理学研究科, 教授 (50143160)
TAKIZAWA Yumi  Japan Women's University, Institute of Mathematical Statistics, Department of Prediction and Control, Associate Professor, 統計数理研究所・予測制御系, 助教授 (90280528)
中神 祥臣  日本女子大学, 理学部, 教授 (70091246)
峰村 勝弘  日本女子大学, 理学部, 教授 (20060684)
中神 潤一  千葉大学, 理学部, 教授 (30092076)
安田 正実  千葉大学, 理学部, 教授 (00041244)
田栗 正章  千葉大学, 理学部, 教授 (10009607)
山本 光晴  千葉大学, 理学部, 助手 (00291295)
Project Period (FY) 2001 – 2004
Project Status Completed (Fiscal Year 2004)
Budget Amount *help
¥3,500,000 (Direct Cost: ¥3,500,000)
Fiscal Year 2004: ¥600,000 (Direct Cost: ¥600,000)
Fiscal Year 2003: ¥700,000 (Direct Cost: ¥700,000)
Fiscal Year 2002: ¥900,000 (Direct Cost: ¥900,000)
Fiscal Year 2001: ¥1,300,000 (Direct Cost: ¥1,300,000)
Keywordsimproved estimators / two-sample problems / covariance matrix / simultaneous estimation / growth curve / スタイン推定量 / 縮小推定 / グラフィカルモデル / 同時推定
Research Abstract

It is well-known that the sample mean and the sample covariance matrix are inadmissible under assumption of normality and appropriate loss function (This is called Stein effect or shrinkage methods.). Since discovery of this phenomenon, there has been a large body of studies on this topic. Furthermore, there has been a broad attention on so called Stein's unbiased risk estimate (SURE), which has been originally proposed for a method to evaluate risk function of estimators under consideration, beyond the original purpose. Although such new development has been reported recently, there are many problems in multivariate analysis with complex structure to be considered based on shrinkage method. The purpose of our research is to develop shrinkage method in complex multivariate model.
In this year we investigate on following statistical models and develop shrinkage estimators :
(1)We have considered the problem of estimating common regression coefficient matrix of two growth curve models and proposed new shrinkage estimators. Furthermore, we demonstrate numerical experiment to indicate that our proposed estimators have better performance over known estimators.
(2)We have considered the problem of estimating a precision matrix of the multivariate normal distribution under the squared loss function and obtained improved estimators.
(3)Applying theory of symmetric cones and generalized Wishart distributions, we have developed improved estimation method including the problem of estimating covariance matrix of complex Wishart distribution.

Report

(5 results)
  • 2004 Annual Research Report   Final Research Report Summary
  • 2003 Annual Research Report
  • 2002 Annual Research Report
  • 2001 Annual Research Report
  • Research Products

    (9 results)

All 2005 2004 Other

All Journal Article (2 results) Publications (7 results)

  • [Journal Article] Alternative estimators of the common regression matrix in two GMANOVA models under weighted quadratic losses2005

    • Author(s)
      H.Tsukuma
    • Journal Title

      Journal of Statistical Planning and Inference (印刷中)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Annual Research Report 2004 Final Research Report Summary
  • [Journal Article] Alternative estimators of the common regression matrix in two GMANOVA models under weighted quadratic loss2004

    • Journal Title

      Journal of Statistical Planning and Inference, Corrected Proof, Available online 23 November 23(In press)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Publications] H.Tsukuma: "Modifying the Graybill-Deal estimator of the common regression matrix in two growth curve models."数理解析研究所講究録. 1334. 95-111 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] H.Tsukuma: "Simultaneous estimation of scale matrices in two-sample problem under elliptically contoured distributions."J.f the Japanese Society of Computational Statistics. 16(印刷中). (2004)

    • Related Report
      2003 Annual Research Report
  • [Publications] Tsukuma, H.: "Simultaneous estimation of scale matrices in two-sample problem under elliptically contoured distributions"J. of Japanese Society of Computational Statistics. (発表予定).

    • Related Report
      2002 Annual Research Report
  • [Publications] Konno, Y.: "Inadmissibility of maximum likelihood estimator"Journal of multivariate analysis. 79・1. 33-51 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] Shiraish, T.: "Robust estimates of location parameters in two-way layouts with interaction"Journal of the Japanese Society of Computational Statistics. 14・1. 1-9 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] Hashimoto, A.: "Correction maximization under linear and quadratic constraints"Bulletin of the International Statistical Institute,53rd session. 117-118 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] Sakurai, H.: "Bootstrap estimation for swap-rate by preliminary selection in university entrance examination"Bulletin of International Statistical Institute,53rd session. 235-236 (2001)

    • Related Report
      2001 Annual Research Report

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

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