Development of two-stage methods for non-normal populations

• Project/Area Number: 21500278
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Statistical science
• Research Institution: Hiroshima University
• Principal Investigator: WAKAKI Hirofumi 広島大学, 大学院・理学研究科, 教授 (90210856)
• Project Period (FY): 2009 – 2011
• Project Status: Completed (Fiscal Year 2011)
• Budget Amount: ¥3,640,000 (Direct Cost: ¥2,800,000、Indirect Cost: ¥840,000); Fiscal Year 2011: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2010: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000); Fiscal Year 2009: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
• Keywords: 2段階標本抽出 / 漸近展開 / 単調変換 / ブートストラップ / 2段階法 / 非正規母集団 / ブートストラップ法 / 検定方法の選択 / 局所対立仮説

Research Abstract

Two new methods of two-stage procedure of constructing a confidence region of the mean vector for non-normal populations are suggested. The one is a method using asymptotic expansion of the distribution, and the other is a method using a bootstrap method. We clarified character of each methods including their drawback. We found another bootstrap method to overcome a problem of over estimating the sample size needed in the original Healy' s two-stage method

Research Products

• [Journal Article] Asymptotic expansions for a class of tests for a general covariance structure undera local alternative (2011)
  • Author(s): Shimizu, H. and Wakaki, H.
  • Journal Title: Journal of Multivariate Analysis Volume: 102 Pages: 1080-1089
  • Peer Reviewed
• [Journal Article] Asymptotic expansions for a class of tests for a general covariance structure under a local alternative (2011)
  • Author(s): H.Shimizu, H.Wakaki
  • Journal Title: Journal of Multivariate Analysis Volume: 102 Pages: 1080-1089
  • Peer Reviewed
• [Journal Article] High{ dimensional Edgeworth expansion of a test statistic on independence and its error bound (2010)
  • Author(s): Akita, T., Jin, J., and Wakaki, H.
  • Journal Title: Journal of Multivariate Analysis Volume: 101 Pages: 1806-1813
  • Peer Reviewed
• [Journal Article] Asymptotic expansions for a class of tests for a general covariance structure under a local alternative (2010)
  • Author(s): Hiroaki Shimizu, Hirofumi Wakaki
  • Journal Title: Hiroshima Statistical Group Techinical Report Volume: TR10-05 Pages: 1-16
• [Presentation] Box型大標本漸近展開近似の誤差限界 (2011)
  • Author(s): 若木宏文
  • Organizer: 統計関連学会連合大会
  • Place of Presentation: アクロス福岡
  • Year and Date: 2011-09-05
• [Presentation] 正準相関分析の追加情報の冗長性に関する検定統計量の分布の漸近展開近似の誤差評価 (2010)
  • Author(s): 若木宏文、藤越康祝
  • Organizer: 統計関連学会連合大会
  • Place of Presentation: 早稲田大学早稲田キャンパス
  • Year and Date: 2010-09-06
• [Presentation] 正準相関分析の追加情報の冗長性に関する検定統計量の分布の漸近展開近似の誤差評価 (2010)
  • Author(s): 若木宏文, 若木宏文
  • Organizer: 2010年度統計関連学会連合大会
  • Place of Presentation: 早稲田大学
  • Year and Date: 2010-09-06
• [Presentation] An asymptotic expansion of the local power of a general test for testing a general covariance structure (2009)
  • Author(s): A. Shimizu and H. Wakaki
  • Organizer: Hirhoshima Research Group Seminor
  • Place of Presentation: Hiroshima
  • Year and Date: 2009-10-30
• [Presentation] Asymptotic expansions for a class of tests for a general covariance structure under a local alternative (2009)
  • Author(s): 清水暁裕、秋田智之、若木宏文
  • Organizer: 統計関連学会連合大会
  • Place of Presentation: 同志社大学京田辺キャンパス
  • Year and Date: 2009-09-08
• [Presentation] An asymptotic expansion of the local power of a general test for testing a general covariance structure (2009)
  • Author(s): Hirofumi Wakaki
  • Organizer: STOCHASTIC ANALYSIS OF THE ADVANCED STATISTICAL MODELS
  • Place of Presentation: Steklov Mathematical Institute (Moscow)
  • Year and Date: 2009-09-05
• [Presentation] 非正規母集団に対する二段階標本抽出法 (2009)
  • Author(s): 若木宏文、青嶋誠
  • Organizer: 広島統計グループ金曜セミナー
  • Place of Presentation: 広島大学理学部
  • Year and Date: 2009-07-24
• [Book] 確率・統計の数学的基礎 (2011)
  • Author(s): 藤越康祝, 若木宏文, 柳原宏和
  • Total Pages: 373
  • Publisher: 広大出版会
• [Remarks] 広島大学理学部数学科数理統計グループのホームページ(セミナー、テクニカルレポート等の情報)
  • URL: http://www.math.sci.hiroshima-u.ac.jp/stat/