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The mathematical theory of statistical multiple comparisons

Research Project

Project/Area Number 24540148
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field General mathematics (including Probability theory/Statistical mathematics)
Research InstitutionNanzan University

Principal Investigator

SHIRAISHI Taka-aki  南山大学, 理工学部, 教授 (50143160)

Project Period (FY) 2012-04-01 – 2016-03-31
Project Status Completed (Fiscal Year 2015)
Budget Amount *help
¥3,640,000 (Direct Cost: ¥2,800,000、Indirect Cost: ¥840,000)
Fiscal Year 2015: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2014: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2013: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2012: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Keywords多重比較検定法 / 閉検定手順 / 同時信頼区間 / 分布論 / 数値解析 / 多重比較法 / 正規分布論 / ノンパラメトリック法 / 漸近理論 / 統計的多重比較論 / ノンパラメトリック論 / 数理統計 / 計算機統計 / 生物統計
Outline of Final Research Achievements

We derived the following conclusions (i)-(iv) for multiple comparison procedures in multi-sample models. (i) Suppose that the simple order restriction of means is satisfied under the underlying normal distribution. Then, for the differences among mean responses, a closed testing procedure is superior to the single step Hayter's test (Hayter (1990)). To compute the upper percentiles of the distributions of statistics, the sinc method described in Lund and Bowers (1992) and Stenger (1993) is utilized. (ii) Suppose that the underlying distribution is a normal distribution function with unequal variances. Then, for the differences among mean responses, Shiraishi and Hayakawa (2015) propose a closed testing procedure superior to the single step Games-Howell test. (iii) Suppose that the underlying distribution is unknown. Then nonparametric multiple comparison procedures are discussed. (iv) Under Bernoulli distribution, the theory of multiple comparison procedures are constructed.

Report

(5 results)
  • 2015 Annual Research Report   Final Research Report ( PDF )
  • 2014 Research-status Report
  • 2013 Research-status Report
  • 2012 Research-status Report
  • Research Products

    (15 results)

All 2016 2015 2014 2013 2012 Other

All Journal Article (8 results) (of which Peer Reviewed: 8 results,  Acknowledgement Compliant: 4 results,  Open Access: 2 results) Presentation (3 results) (of which Invited: 3 results) Book (1 results) Remarks (3 results)

  • [Journal Article] 順序制約のある場合のすべての平均相違に対したBartholomewの検定に基づく閉検定手順2016

    • Author(s)
      白石高章, 松田眞一
    • Journal Title

      日本統計学会誌

      Volume: 45 Pages: 247-271

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] 順序制約のある場合の対照群との比較におけるカイバー自乗統計量に基づく多重比較検定法2015

    • Author(s)
      白石高章, 松田眞一
    • Journal Title

      計量生物学

      Volume: 36 Pages: 85-99

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] 平均母数に傾向性がある正規多群モデルにおける多重比較法に使用される分布の上側100α⋆ パーセント点2015

    • Author(s)
      白石高章,杉浦洋
    • Journal Title

      日本統計学会誌

      Volume: 44 Pages: 271-314

    • Related Report
      2014 Research-status Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] 母分散が一様でない多群モデルにおけるすべての母平均相違の閉検定手順2014

    • Author(s)
      白石高章,早川由宏
    • Journal Title

      計量生物学

      Volume: 35 Pages: 55-68

    • NAID

      130005129822

    • Related Report
      2014 Research-status Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] 多群連続モデルにおける位置母数に順序制約のある場合の閉検定手順2014

    • Author(s)
      白石高章
    • Journal Title

      日本統計学会和文誌

      Volume: 43 Pages: 215-245

    • NAID

      110009807032

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] 順序制約のある場合の多群比率モデルにおける多重比較法2014

    • Author(s)
      白石高章
    • Journal Title

      応用統計学

      Volume: 43 Pages: 20-20

    • NAID

      130005069597

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] 多群指数モデルにおける平均パラメータの多重比較法2013

    • Author(s)
      白石高章
    • Journal Title

      日本計量生物学会

      Volume: 34 Pages: 1-20

    • NAID

      10031194712

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] 多群の2 項モデルとポアソンモデルにおけるすべてのパラメータの多重比較法2012

    • Author(s)
      白石高章
    • Journal Title

      日本統計学会誌

      Volume: 第42巻 Pages: 55-90

    • NAID

      110009543879

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Presentation] 多群モデルにおける多重比較法の発展的理論2015

    • Author(s)
      白石高章
    • Organizer
      日本数学会2015年度年会
    • Place of Presentation
      明治大学 駿河台キャンパスリバティタワー2階1022(東京都千代田区神田駿河台1-1)
    • Year and Date
      2015-03-23
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] 多重比較法のトピックス2012

    • Author(s)
      白石高章
    • Organizer
      科研費シンポジウム「医学統計と数理の接点を探る」
    • Place of Presentation
      南山大学
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] 平均母数に順序制約のある場合の閉検定手順

    • Author(s)
      白石高章
    • Organizer
      日本統計学会春季集会
    • Place of Presentation
      同志社大学
    • Related Report
      2013 Research-status Report
    • Invited
  • [Book] 統計科学の基礎 - デ-タと確率の結びつきがよくわかる数理2012

    • Author(s)
      白石高章
    • Total Pages
      272
    • Publisher
      日本評論社
    • Related Report
      2012 Research-status Report
  • [Remarks] 研究者詳細 - 白石 高章 - NZ: Porta

    • URL

      https://porta.nanzan-u.ac.jp/research/view?l=ja&u=102104

    • Related Report
      2015 Annual Research Report
  • [Remarks] Shiraishi's Web Site

    • URL

      http://www.seto.nanzan-u.ac.jp/~marble/

    • Related Report
      2013 Research-status Report
  • [Remarks] 研究者詳細

    • URL

      https://porta.nanzan-u.ac.jp/research/view?l=ja&u=102104

    • Related Report
      2013 Research-status Report

URL: 

Published: 2013-05-31   Modified: 2019-07-29  

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