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Studies on.the structure of.methods, of.sequential estimation

Research Project

Project/Area Number 14540107
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 InstitutionNIIGATA UNIVERSITY

Principal Investigator

ISOGAI Eiichi  NIIGATA UNIVERSITY, Fac.of Science, Prof., 理学部, 教授 (40108014)

Co-Investigator(Kenkyū-buntansha) AKASHI Shigeo  Science Univ.of Tokyo, Fac.of Science & Tech., Prof., 理工学部, 教授 (30202518)
TERASAWA Tatsuo  NIIGATA UNIVERSITY, Fac.of Science, Prof., 理学部, 教授 (00197790)
AKAHIRA Masafumi  Univ.of Tsukuba, Inst.of Math., Prof., 数学系, 教授 (70017424)
SUZUKI Tomonari  NIIGATA UNIVERSITY, Graduate School of Science and Tech., Assistant, 大学院・自然科学研究科, 助手 (00303173)
UNO Chikara  Akita Univ., Fac.of Education, and Human Studies Associate, Associate Prof., 教育文化学部, 助教授 (20282155)
Project Period (FY) 2002 – 2003
Project Status Completed (Fiscal Year 2003)
Budget Amount *help
¥3,600,000 (Direct Cost: ¥3,600,000)
Fiscal Year 2003: ¥1,500,000 (Direct Cost: ¥1,500,000)
Fiscal Year 2002: ¥2,100,000 (Direct Cost: ¥2,100,000)
Keywordssequential estimation / fully sequential procedure / power of scale parameter / bounded risk / normal distribution / exponential distribution / second-order asymptotic expansion / bias adjustment / 停止規則 / 尺度母数 / リグレット / 最小危険 / 逐次手法
Research Abstract

Head Investigator and each of the investigators obtained the research results concerning the title of this project directly or indirectly. The main results by head investigator are as follows.
(1)We consider the point estimation problem of the powers of a standard deviation of a normal distribution with unknown mean and variance when the loss function is squared error plus linear cost. When we estimate them by using the smallest sample size such that the risk is minimized, the asymptotic optimal sample size contains the unknown parameter. Therefore we propose a sequential estimator and obtain the asymptotic expansions of the expected sample size and the risk of the sequential estimator as the cost per unit sample approaches zero.
(2)We consider the point estimation problem of the powers of scale parameter of a normal distribution. We want to estimate the powers by using the smallest sample size such that the risk is less than or equal to a preassigned error bound when the risk is mean squared error. In this case the asymptotic optimal sample size contains the unknown parameter. Therefore we define a stopping rule and show that the risk is less than or equal to the error bound. Also, we consider the problem of estimating a scale parameter of an exponential distribution when the loss function is squared error plus linear cost.
(3)We consider the bounded risk point estimation problem of the powers of scale parameter of an exponential distribution. We want to estimate the powers by using the smallest sample size such that the risk is less than or equal to a preassigned error bound when the risk is mean squared error. This smallest sample size cannot be used in practice, because it contains the unknown parameter. Therefore we propose a stopping rule and show that the condition of the risk is satisfied for sufficiently small error bound.

Report

(3 results)
  • 2003 Annual Research Report   Final Research Report Summary
  • 2002 Annual Research Report
  • Research Products

    (37 results)

All Other

All Publications (37 results)

  • [Publications] Chikara Uno: "Sequential point estimation of the powers of a normal scale parameter"Metrika. 55. 215-232 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Masafumi Akahira: "Information inequalities for the Bayes risk for a family of non-regular distributions"Annals of the Institute of Statistical Mathematics. 54. 806-815 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Tomonari Suzuki: "Strong convergence theorem to common fixed points of two nonexpansive mappings in general Banach spaces"Journal of Nonlinear and Convex Analysis. 3. 381-391 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Tomonari Suzuki: "On strong convergence to common fixed points of nonexpansive semigroups in Hilbert spaces"Proceedings of the American Mathematical Society. 131. 2133-2136 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Eiichi Isogai: "Sequential estimation of the powers of normal and exponential scale parameters"Sequential Analysis. 22. 129-149 (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Muktar Ali: "Sequential point estimation of the powers of an exponential scale parameter"Scientiae Mathematicae Japonicae. 58. 39-53 (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Masafumi Akahira: "The information inequality in sequential estimation for the uniform case"Sequential Analysis. 22. 223-232 (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Hidekazu Tanaka: "On a family of distributions attaining the Bhattacharyya bound"Annals of the Institute of Statistical Mathematics. 55. 309-317 (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Eisuke Hida: "An approximation to the generalized hypergeometric distribution"Statistical Papers. 44. 483-497 (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Shigeo Akashi: "A version of Hilbert's 13th problem for analytic functions"Bulletin of the London Mathematical Society. 35. 8-14 (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Chikara Uno: "Sequential estimation of the ratio of scale parameters in the exponential two-sample problem"Journal of the Japan Statistical Society. 33. 231-244 (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Tomonari Suzuki: "On Downing-Kirk's theorem"Journal of Mathematical Analysis and Applications. 286. 453-458 (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Tomonari Suzuki: "Convergence theorems to common fixed points for infinite families of nonexpansive mappings in strictly convex Banach spaces"Nihonkai Mathematical Journal. 14. 43-54 (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] C.Uno, E.Isogai: "Sequential point estimation of the powers of a normal scale parameter"Metrika. 55. 215-232 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] M.Akahira, N.Ohyauchi: "Information inequalities for the Bayes risk for a family of non-regular distributions"Ann.Inst.Statist.Math. 54. 806-815 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] T.Suzuki: "Strong convergence theorem to common fixed points of two nonexpansive mappings in general Banach spaces"J.Nonlinear Convex Anal.. 3. 381-391 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] T.Suzuki: "On strong convergence to common fixed points of nonexpansive semigroups in Hilbert spaces"Proc.Amer Math.Soc.. 131. 2133-2136 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] E.Isogai, M.Ali, C.Uno: "Sequential estimation of the powers of normal and exponential scale parameters"Sequential Anal.. 22. 129-149 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] M.Ali, E.Isogai: "Sequential point estimation of the powers of an exponential scale parameter"Sci.Math.Jpn. 58. 39-53 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] M.Akahira, K.Takeuchi: "The information inequality in sequential estimation for the uniform case"Sequential Anal.. 22. 223-232 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] H.Tanaka, M.Akahira: "On a family of distributions attaining the Bhattacharyya bound"Ann.Inst.Statist.Math. 55. 309-317 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] E.Hida, M.Akahira: "An approximation to the generalized hypergeometric distribution"Statist.Papers. 44. 483-497 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] S.Akashi: "A version of Hilbert's 13th problem for analytic functions"Bull.London Math.Soc.. 35. 8-14 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] C.Uno: "Sequential estimation of the ratio of scale parameters in the exponential two-sample problem"J.Japan Statist.Soc.. 33. 231-244 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] T.Suzuki: "On Downing-Kirk's theorem"J.Math.Anal.Appl.. 286. 453-458 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] T.Suzuki: "Convergence theorems to common fixed points for infinite families of nonexpansive mappings in strictly convex Banach spaces"Nihonkai Math.J.. 14. 43-54 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Eisuke Hida: "An approximation to the generalized hypergeometric distribution"Statistical Papers. 44. 483-497 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] Hidekazu Tanaka: "On a family of distributions attaining the Bhattacharyya bound"Ann.Inst.Statist.Math.. 55・2. 309-317 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] Masafumi Akahira: "The information inequality in sequential estimation for the uniform case"Sequential Anal.. 22・3. 223-232 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] Chikara Uno: "Sequential estimation of the ratio of scale parameters in the exponential two-sample problem"J.Japan.Statist.Soc.. 33・2. 231-244 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] Tomonari Suzuki: "Convergence theorems to common fixed points for infinite families of nonexpansive mappings in strictly convex Banach spaces"Nihonkal Math.J.. 14・1. 43-54 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] Tomonari Suzuki: "On Downing-Kirk's theorem"J.Math.Anal.Appl.. 286. 453-458 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] Shigeo Akashi: "A version of Hilbert's 13th problem for analytic functions"Bull.London Math.Soc.. 35. 8-14 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] Eiichi Isogai: "Sequential estimation of the powers of normal and exponential scale parameters"Sequential analysis. 22・1(印刷中). (2003)

    • Related Report
      2002 Annual Research Report
  • [Publications] Muktar Ali: "Sequential point estimation of the powers of exponential scale parameter"Scientiae Mathematicae Japanicae Online. 8. 71-85 (2003)

    • Related Report
      2002 Annual Research Report
  • [Publications] Masafumi Akahira: "Information inequalities for the Bayes risk for a family of non-regular distributions"Ann. Inst. Statist. Math.. 54・4. 806-815 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] Tomonari Suzuki: "Strong convergence theorem to common fixed points of two non expansive mappings in general Banach spaces"J. Non Linear Convex Analysis. 3. 381-391 (2002)

    • Related Report
      2002 Annual Research Report

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Published: 2002-04-01   Modified: 2016-04-21  

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