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Evaluation of the performance of stopping rules in sequential analysis

Research Project

Project/Area Number 20540102
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 InstitutionAkita University

Principal Investigator

UNO Chikara  秋田大学, 教育文化学部, 教授 (20282155)

Co-Investigator(Kenkyū-buntansha) HIRATA Kentaro  秋田大学, 教育文化学部, 准教授 (30399795)
SUZUKI Masaaki  秋田大学, 教育文化学部, 准教授 (70431616)
Project Period (FY) 2008 – 2011
Project Status Completed (Fiscal Year 2011)
Budget Amount *help
¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000)
Fiscal Year 2011: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2010: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2009: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2008: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Keywords二段階法 / 逐次推定 / 漸近有効性 / リグレット / 統計数学 / 漸近一致性 / 区間推定 / 停止規則 / 逐次解析
Research Abstract

There are some problems of statistical inference for which no procedures of fixed sample size are available. For example, the problem of constructing fixed-width confidence interval for the mean of a population with confidence level 95% corresponds to it. For this case, we can solve the problem by means of a sequential sampling method where the size of sample is randomly given. In this research, we considered the problem of evaluating the performance of two-stage estimation procedure, provided the unknown variance has the known lower bound, and established a theory which gives more exact evaluation than precedent research.

Report

(6 results)
  • 2011 Annual Research Report   Final Research Report ( PDF )
  • 2010 Annual Research Report   Self-evaluation Report ( PDF )
  • 2009 Annual Research Report
  • 2008 Annual Research Report
  • Research Products

    (24 results)

All 2012 2011 2010

All Journal Article (12 results) (of which Peer Reviewed: 9 results) Presentation (12 results)

  • [Journal Article] Asymptotic properties of a two-stage procedure for two negative exponential distributions2012

    • Author(s)
      Eiichi Isogai, Chikara Uno, Daisy Lou Polestico
    • Journal Title

      Pioneer Journal of Theoretical and Applied Statistics

      Volume: (in press)

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Higher than second order approximations for sequential point estimation by a two-stage procedure2012

    • Author(s)
      Chikara Uno, Eiichi Isogai
    • Journal Title

      Statistics

      Volume: (in press)

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Two-stage procedure having exact third-order properties for anormal mean2012

    • Author(s)
      Eiichi Isogai, Chikara Uno, Daisuke Takeuchi
    • Journal Title

      Communications in Statistics-Theory and Methods

      Volume: (in press)

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Higher than second order approximations for sequential point estimation by a two-stage procedure2012

    • Author(s)
      Chikara Uno
    • Journal Title

      Statistics

      Volume: (印刷中)

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Asymptotic properties of a two-stage procedure for two negative exponential distributions2012

    • Author(s)
      Eiichi Isogai
    • Journal Title

      Pioneer Journal of Theoretical and Applied Statistics

      Volume: (印刷中)

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Higher order approximations by a two-stage procedure for a negative exponential distribution2011

    • Author(s)
      Eiichi Isogai, Kana Kobayashi, Chikara Uno
    • Journal Title

      Journal of Statistical Planning and Inference

      Volume: Vol.141 Pages: 3304-3312

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] 正規分布の母平均の逐次区間推定に対する2段階法による3次近似式2011

    • Author(s)
      磯貝英一, 宇野力, 竹内大輔
    • Journal Title

      京都大学数理解析研究所講究録

      Volume: 1758巻 Pages: 129-135

    • Related Report
      2011 Final Research Report
  • [Journal Article] Higher order approximations by a two-stage procedure for a negative exponential distribution2011

    • Author(s)
      Eiichi Isogai
    • Journal Title

      Journal of Statistical Planning and Inference

      Volume: 141 Pages: 3304-3312

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] 正規分布の母平均の逐次区間推定に対する2段階法による3次近似式2011

    • Author(s)
      磯貝英一、宇野力、竹内大輔
    • Journal Title

      京都大学数理解析研究所講究録 印刷中

    • Related Report
      2010 Self-evaluation Report
  • [Journal Article] Two-stage procedure having exact third-order properties for a normal mean2011

    • Author(s)
      Eiichi Isogai, Chikara Uno, Daisuke Takeuchi
    • Journal Title

      Communications in Statistics-Theory and Methods in press

    • Related Report
      2010 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] Two-stage procedure having exact third-order properties for a normal mean2011

    • Author(s)
      Eiichi Isogai
    • Journal Title

      Communications in Statistics, Theory and Methods

      Volume: in press

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] 正規分布の母平均の逐次区間推定に対する2段階法による3次近似式2011

    • Author(s)
      磯貝英一
    • Journal Title

      京都大学数理解析研究所講究録

      Volume: 印刷中

    • Related Report
      2010 Annual Research Report
  • [Presentation] 二段階法による正規分布の分散の最小リスク問題2012

    • Author(s)
      磯貝英一, 宇野力
    • Organizer
      RIMS共同研究「A New Perspective to Statistical Models and Related Topics」(研究代表者:赤平昌文)
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2012-03-06
    • Related Report
      2011 Final Research Report
  • [Presentation] 二段階法による正規分布の分散の最小リスク問題2012

    • Author(s)
      磯貝英一
    • Organizer
      A New Perspective to Statistical Models and Related Topics
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2012-03-06
    • Related Report
      2011 Annual Research Report
  • [Presentation] Higher order properties of a two-stage procedure for estimating the difference of location parameters of two negative exponential distributions2011

    • Author(s)
      磯貝英一, 宇野力, Daisy Lou Polestico
    • Organizer
      研究会「統計的推測の理論と方法論,及び,最近の動向」(研究代表者:青嶋誠、赤平昌文)
    • Place of Presentation
      筑波大学
    • Year and Date
      2011-11-08
    • Related Report
      2011 Final Research Report
  • [Presentation] Higher order properties of a two-stage procedure for estimating the difference of location parameters of two negative exponential distributions2011

    • Author(s)
      磯貝英一
    • Organizer
      統計的推測の理論と方法論,及び,最近の動向
    • Place of Presentation
      筑波大学
    • Year and Date
      2011-11-08
    • Related Report
      2011 Annual Research Report
  • [Presentation] On asymptotic higher-order expansions by a two-stage procedure2011

    • Author(s)
      Chikara Uno, Eiichi Isogai
    • Organizer
      58^<th> World Statistics Congress of the International Statistical Institute
    • Place of Presentation
      Convention Centre Dublin, Ireland
    • Year and Date
      2011-08-25
    • Related Report
      2011 Final Research Report
  • [Presentation] On asymptotic higher-order expansions by a two-stage procedure2011

    • Author(s)
      Chikara Uno
    • Organizer
      58^<th> World Statistics Congress of the International Statistical Institute
    • Place of Presentation
      アイルランド共和国ダブリン市コンベンションセンター
    • Year and Date
      2011-08-25
    • Related Report
      2011 Annual Research Report
  • [Presentation] 正規分布の母平均の逐次区間推定に対する2段階法による3次近似式2011

    • Author(s)
      磯貝英一, 宇野力, 竹内大輔
    • Organizer
      RIMS共同研究「Statistical Information in Inference and Its Related Topics」(研究代表者:赤平昌文)
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2011-03-08
    • Related Report
      2011 Final Research Report
  • [Presentation] 正規分布の母平均の逐次区間推定に対する2殺階法による3次近似式2011

    • Author(s)
      磯貝英一、宇野力、竹内大輔
    • Organizer
      RIMS共同研究Statistical Information in Inference and Its Related Topics(研究代表者:赤平昌文)
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2011-03-08
    • Related Report
      2010 Self-evaluation Report
  • [Presentation] 正規分布の母平均の逐次区間推定に対する2段階法による3次近似式2011

    • Author(s)
      磯貝英一
    • Organizer
      Statistical Information in Inference and Its Related Topics
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2011-03-08
    • Related Report
      2010 Annual Research Report
  • [Presentation] Higherorder approximation by a two-stage procedure for a negative exponential distribution2010

    • Author(s)
      磯貝英一, 小林加奈, 宇野力
    • Organizer
      シンポジウム「統計的推測方法の理論的展開とその応用」(研究代表者:谷口正信)
    • Place of Presentation
      熊本大学
    • Year and Date
      2010-11-18
    • Related Report
      2011 Final Research Report
  • [Presentation] Higher order approximation by a two-stage procedure for a negative exponential distribution2010

    • Author(s)
      磯貝英一、小林加奈、宇野力
    • Organizer
      平成22年度科学研究費基盤研究(A)によるシンポジウム「統計的推測方法の理論的展開とその応用」(研究代表者:谷口正信)
    • Place of Presentation
      熊本大学
    • Year and Date
      2010-11-18
    • Related Report
      2010 Self-evaluation Report
  • [Presentation] Higher order approximations by a two stage procedure for a negative exponential distribution2010

    • Author(s)
      磯貝英一
    • Organizer
      統計的推測方法の理論的展開とその応用
    • Place of Presentation
      熊本大学
    • Year and Date
      2010-11-18
    • Related Report
      2010 Annual Research Report

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Published: 2008-04-01   Modified: 2016-04-21  

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