Methodology of sequential procedures and its applications

• Project/Area Number: 23540128
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: General mathematics (including Probability theory/Statistical mathematics)
• Research Institution: Niigata University
• Principal Investigator: ISOGAI Eiichi 新潟大学, 自然科学系, フェロー (40108014)
• Project Period (FY): 2011 – 2013
• Project Status: Completed (Fiscal Year 2013)
• Budget Amount: ¥3,380,000 (Direct Cost: ¥2,600,000、Indirect Cost: ¥780,000); Fiscal Year 2013: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000); Fiscal Year 2012: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2011: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
• Keywords: 統計数学 / 逐次解析 / 二段階法 / 信頼区間問題 / 最小リスク問題 / 高次漸近展開 / 平均標本数 / リグレット / 被覆確率 / 指数分布，正規分布 / ２段階法 / 純逐次法 / 逐次信頼区間 / 最小リスク / 有界リスク / 高次漸近有効性 / 信頼区間 / 漸近有効性 / 正規分布 / 指数分布

Research Abstract

The main results which head investigator obtained are as follows.
(1) We consider the problem of fixed-width confidence interval estimation of a location parameter of a negative exponential distribution under the assumption that a positive lower bound of a scale parameter is known. Using the two-stage procedure proposed by Mukhopadhyay and Duggan (1999) we provided higher order asymptotic expansions of the average sample number and coverage probability. (2011) (2) We considered the minimum risk point estimation problem for the mean and variance of a normal population under the assumption that a positive lower bound of an unknown variance is known. By using two-stage procedure we gave higher than second-order approximations of the average sample number and regret.(2013)

Research Products

• [Journal Article] Higher than second-order approximations for sequential point estimation by a two-stage procedure (2013)
  • Author(s): C. Uno and E. Isogai
  • Journal Title: Statistics Volume: Vol.47 Issue: 2 Pages: 306-316
  • DOI: 10.1080/02331888.2011.588710
  • Peer Reviewed
• [Journal Article] Minimum risk point estimation for the normal variance by a two-stage procedure and second-order properties (2013)
  • Author(s): E. Isogai and C. Uno
  • Journal Title: Journal of Statistics : Advances in Theory and Applications Volume: Vol.9 Pages: 55-72
  • URL: http://scientificadvances.co.in/
  • Peer Reviewed
• [Journal Article] Minimum risk point estimation for the normal variance by a two-stage procedure and second-order properties (2013)
  • Author(s): Eiichi Isogai and Chikara Uno
  • Journal Title: Journal of Statistics: Advances in Theory and Applications Volume: 9 Pages: 55-72
  • Peer Reviewed
• [Journal Article] Two-stage procedure having exact third-order properties for a normal mean (2012)
  • Author(s): Eiichi Isogai, Chikara Uno and Daisuke Takeuchi
  • Journal Title: Communications in Statistics - Theory and Methods Volume: 41 Issue: 23 Pages: 4332-4347
  • DOI: 10.1080/03610926.2011.573166
  • Peer Reviewed
• [Journal Article] Asymptotic properties of a two-stage procedure and their applications (2012)
  • Author(s): C. Uno and E. Isogai
  • Journal Title: Far East Journal of Theoretical Statistics Volume: Vol.40 Pages: 75-105
  • URL: http://pphmj.com/journals/fjts.html
  • Peer Reviewed
• [Journal Article] On second-order approximations to the risk in estimating the exponential mean by a two-stage procedure (2012)
  • Author(s): E. Isogai and C. Uno
  • Journal Title: International Journal of Statistics and Probability Volume: Vol.1 Issue: 2 Pages: 47-55
  • DOI: 10.5539/ijsp.v1n2p47
  • Peer Reviewed
• [Journal Article] Asymptotic properties of a two-stage procedure for two negative exponential distributions (2012)
  • Author(s): E. Isogai, C. Uno and Daisy Lou Polestico
  • Journal Title: Pioneer Journal of Theoretical and Applied Statistics Volume: Vol.3 Pages: 31-56
  • URL: http://www.pspchv.com/content_PJTAS.html
  • Peer Reviewed
• [Journal Article] Asymptotic properties of a two-stage procedure and their applications (2012)
  • Author(s): Chikara Uno and Eiichi Isogai
  • Journal Title: Far East Journal of Theoretical Statistics Volume: 40 Pages: 75-105
  • Peer Reviewed
• [Journal Article] On second-order approximations to the risk in estimating the exponential mean by a two-stage procedure (2012)
  • Author(s): Eiichi Isogai and Chikara Uno
  • Journal Title: International Journal of Statistics and Probability Volume: 1 Pages: 47-55
  • Peer Reviewed
• [Journal Article] Asymptotic properties of a two-stage procedure for two negative exponential distributions (2012)
  • Author(s): Eiichi Isogai, Chikara Uno and Daisy Lou Polestico
  • Journal Title: Pioneer Journal of Theoretical and Applied Statistics Volume: 3 Pages: 31-56
  • Peer Reviewed
• [Journal Article] Higher order approximations by a two-stage procedure for a negative exponential distribution (2011)
  • Author(s): E. Isogai, K. Kobayashi and C. Uno
  • Journal Title: Journal of Statistical Planning and Inference Volume: Vol.141 Issue: 10 Pages: 3304-3312
  • DOI: 10.1016/j.jspi.2011.04.012
  • Peer Reviewed
• [Presentation] A two-stage procedure for minimum risk point estimation of the mean of an exponential distribution and second-order results (2012)
  • Author(s): 宇野 力
  • Organizer: 第8回確率・統計世界会議
  • Place of Presentation: グランド セバヒルホテル会議場(トルコ)
  • Year and Date: 2012-07-10
• [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: 研究集会「A new perspective to statistical models and related topics」
  • Place of Presentation: 京都大学数理解析研究所
• [Presentation] On asymptotic higher-order expansions by a two-stage procedure (2011)
  • Author(s): 宇野 力
  • Organizer: 第58回国際統計協会会議
  • Place of Presentation: ダブリン国際会議場(アイルランド)
  • Year and Date: 2011-08-25
• [Presentation] On asymptotic higher-order expansions by a two-stage procedure (2011)
  • Author(s): Chikara Uno and Eiichi Isogai
  • Organizer: 第58回 国際統計協会国際会議 (ISI)
  • Place of Presentation: Convention Centre Dublin, Ireland
• [Presentation] Higher order properties of a two-stage procedure for estimating the difference of location parameters of two negative exponential distributions (2011)
  • Author(s): 磯貝 英一，宇野 力，Daisy Lou Polestico
  • Organizer: 研究集会「統計的推論の理論と方法論，及び，最近の動向」
  • Place of Presentation: 筑波大学
• [Presentation] A two-stage procedure for minimum risk point estimation of the mean of an exponential distribution and second-order results
  • Author(s): Chikara Uno
  • Organizer: 第８回 確率統計国際会議
  • Place of Presentation: グランドジェワヒルホテル コンベンションセンター（イスタンブール，トルコ）