Statistical approaches to selection problems

• Project/Area Number: 21540138
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: General mathematics (including Probability theory/Statistical mathematics)
• Research Institution: Kumamoto University
• Principal Investigator: TAKADA Yoshikazu 熊本大学, 大学院・自然科学研究科, 教授 (70114098)
• Project Period (FY): 2009 – 2011
• Project Status: Completed (Fiscal Year 2011)
• Budget Amount: ¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000); Fiscal Year 2011: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000); Fiscal Year 2010: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2009: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
• Keywords: 最良母集団の選択 / 正規分布 / サンプルサイズ / 二段階法 / 三段階法 / Indiference-zone approach / 信頼区間 / 多変量正規分布 / Indifference-zone approach / コントロール / 二段階選択法 / 標準値 / 多段階選択法

Research Abstract

We often encounter the case that we must select one of several groups based on a criterion. If the selection is based on the data obtained through experiments or investigations, it refers to a selection of the best population. In this research we provided three new procedures for the following problems
1. The selection of the best population when there exists a standard or a control.
2. The selection of the best population when there exists a correlation between data
3. The estimation of the parameter after the selection of the best population

Research Products

• [Journal Article] Discussion on "Two-Stage Procedures for High-Dimentional Data" (2011)
  • Author(s): Yoshikazu Takada
  • Journal Title: Sequential Analysis(Makoto Aosima and Kazuyoshi Yata) Volume: 30 Pages: 400-403
  • Peer Reviewed
• [Journal Article] Discussion on "Two-Stage Procedures for High-Dimentional Data" by Makoto Aosima and Kazuyoshi Yata (2011)
  • Author(s): 高田佳和
  • Journal Title: Sequential Analysis Volume: 30 Pages: 400-403
  • Peer Reviewed
• [Journal Article] A three-stage selection procedure with an exact consistency (2010)
  • Author(s): Yoshikazu Takada
  • Journal Title: Communications in Statistics-Theory and Methods Volume: 39 Pages: 1574-1584
  • Peer Reviewed
• [Journal Article] Selecting the best normal population better than a standard under unequal variances (2010)
  • Author(s): Yoshikazu Takada
  • Journal Title: Journal of Statistical Planning and Inference Volume: 140 Pages: 2693-2705
  • Peer Reviewed
• [Journal Article] A three-stage selection procedure with an exact consistency (2010)
  • Author(s): 高田佳和
  • Journal Title: Communications in Statistics-Theory and Methods Volume: VOL.39 Pages: 1574-1584
  • Peer Reviewed
• [Journal Article] Selecting the best normal population better than a standard under unequal variances (2010)
  • Author(s): 高田佳和
  • Journal Title: Journal of Statistical Planning and Inference Volume: VOL.140 Pages: 2693-2705
  • Peer Reviewed
• [Journal Article] Selecting the best component of a Multivariate normal distribution (2009)
  • Author(s): Yoshikazu Takada
  • Journal Title: Communications in Statistics-Theory and Methods Volume: 38 Pages: 3198-3212
  • Peer Reviewed
• [Journal Article] Asymptotically optimal allocation for multiple comparisons with a control when variances are unknown and unequal (2009)
  • Author(s): Makoto Aoshima and Yoshikazu Takada
  • Journal Title: American Journal of Mathematical Management and Science Volume: 29 Pages: 125-137
  • Peer Reviewed
• [Journal Article] Selecting the Best Component of a Multivariate Normal Distribution (2009)
  • Author(s): 高田佳和
  • Journal Title: Communications in Statistics-Theory and Methods VOL.38 Pages: 3198-3212
  • Peer Reviewed
• [Presentation] 最良正規母集団の選択とその母数の推定 (2011)
  • Author(s): 高田佳和
  • Organizer: 研究集会"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(茨城)
  • Year and Date: 2011-11-08
• [Presentation] 等分散を仮定した母平均の差の長さ一定の信頼区間の頑健性について (2011)
  • Author(s): 三山勝也, 高田佳和
  • Organizer: 統計関連学会連合大会
  • Place of Presentation: 九州大学(福岡)
  • Year and Date: 2011-09-06
• [Presentation] 等分散を仮定した母平均の差の長さ一定の信頼区間の頑健性について (2011)
  • Author(s): 三山勝也
  • Organizer: 統計関連学会連合大会
  • Place of Presentation: 九州大学福岡
  • Year and Date: 2011-09-06
• [Presentation] Simultaneous Selection and Estimation of the Largest Normal Mean (2011)
  • Author(s): Yoshikazu Takada
  • Organizer: The 58th Session of the International Statistical Institute
  • Place of Presentation: Dublin(Ireland)
  • Year and Date: 2011-08-25
• [Presentation] Simultaneous Selection and Estimation of the Largest Normal Mean (2011)
  • Author(s): 高田佳和
  • Organizer: The 58th Session of the International Statistical Institute
  • Place of Presentation: Convention Centre Dublin, Dublin, Ireland
  • Year and Date: 2011-08-25
• [Presentation] 標準値がある場合の最良正規母集団の選択-等分散が仮定できない場合 (2009)
  • Author(s): 高田佳和
  • Organizer: 研究集会"統計的推測・確率解析とその周辺の話題の理論と応用"
  • Place of Presentation: 秋田市カレッジプラザ
  • Year and Date: 2009-12-12
• [Presentation] Selecting the best normal population better than a standard under the unequal variance case (2009)
  • Author(s): Yoshikazu Takada
  • Organizer: Second International Workshop in Sequential Methodologies
  • Place of Presentation: Troyes(France)
  • Year and Date: 2009-06-15