Study on multivariate Statistical models and their inference procedures for analysis of high-dimensional data and its applications

• Project/Area Number: 21500283
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Statistical science
• Research Institution: Japan Women's University
• Principal Investigator: KONNO Yoshihiko 日本女子大学, 理学部, 教授 (00205577)
• Project Period (FY): 2009 – 2012
• Project Status: Completed (Fiscal Year 2012)
• Budget Amount: ¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000); Fiscal Year 2012: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2011: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2010: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000); Fiscal Year 2009: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
• Keywords: ウィシャート行列 / 縮小型推定量 / トランケートデータ / ウィシャート分布 / 等質錐 / 多変量解析 / 推測理論 / Stein問題 / 打ち切りデータ / 高次元データ / Wishart分布

Research Abstract

The problem of estimating large covariance matrices of multivariate real normal and complex normal distributions is considered when the dimension of the variables is larger than the number of sample size. The Stein-Haff identities and calculus on eigenstructures for singular Wishart matrices are developed for real and complex cases, respectively. By using these techniques, the unbiased risk estimates for certain class of estimators for the population covariance matrices under an invariant quadratic loss functions are obtained for real and complex cases, respectively.

Research Products

• [Journal Article] goodness-fit test for parametric models based on dependently truncated data (2012)
  • Author(s): Emura, T. and Konno, Y., A
  • Journal Title: Computational Statistics and Data Analysis Volume: vol56 Pages: 2237-2250
• [Journal Article] A goodness-of-fit test for parametric models based on dependently truncated data (2012)
  • Author(s): Takekshi Emura and Yoshihiko Konno
  • Journal Title: Computational Statistics & Data Analysis Volume: 56 Issue: 7 Pages: 2237-2250
  • DOI: 10.1016/j.csda.2011.12.022
  • Peer Reviewed
• [Journal Article] Multivariate normal distribution approaches for dependently left-truncated datta (2012)
  • Author(s): Takeshi Emura, Yoshihiko Konno
  • Journal Title: Statistical Paper Volume: 53 Issue: 1 Pages: 133-149
  • DOI: 10.1007/s00362-010-0321-x
  • Peer Reviewed
• [Journal Article] Estimation of multivariate complex normal covariance under an invariant quadratic loss (2010)
  • Author(s): Konno, Y.
  • Journal Title: Communicationin Statistics--Theory and Method Volume: vol.39 Pages: 1490-1497
• [Journal Article] Estimation of multivariate complex normal covariance under an invariant quadratic loss (2010)
  • Author(s): Y.Konno
  • Journal Title: Communication in Statistics--Theory and Method Volume: 39 Pages: 1490-1497
  • Peer Reviewed
• [Journal Article] Shrinkage estimators for large covariance matrices in multivariate real and complex normal distributions under an invariant quadratics loss (2009)
  • Author(s): Konno, Y
  • Journal Title: Journal of Multivariate Analysis Volume: vol100 Pages: 2237-2253
• [Journal Article] Shrinkage Estimators for Large Covariance matrices in multivariate real and complex normal distributions under an invariant quadratic loss. (2009)
  • Author(s): Yoshihiko Konno
  • Journal Title: Journal of Multivariate Analysis 100 Pages: 2237-3353
  • Peer Reviewed
• [Journal Article] Multivariate normal distributions approaches for dependently left-truncated data
  • Author(s): Emura, T. and Konno, Y.
  • Volume: vol. 53, No. 1
  • Pages: 133-149
• [Presentation] Shrinkage estimators for large covariance matrices in multivariate normal distribution (2012)
  • Author(s): Konno, Y.
  • Organizer: The 2ndims-APRM2012 Meeting
  • Place of Presentation: July 2-4, 2012at Tsukuba
  • Year and Date: 2012-07-03
• [Presentation] Shrinkage estimation of a mean matrix of a multivariate complex normal distribution (2011)
  • Author(s): Yoshihiko Konno
  • Organizer: CIMPA-MICINN-UNESCO Research School
  • Place of Presentation: Hammamet Tunisia
  • Year and Date: 2011-09-08
• [Presentation] Shrinkage estimation of amean matrix of a multivariate complexnormal distribution,CIMPA-MICINN-UNESCO ResearchSchool: Analytical and algebraic tools inStatistics and Graphical Models (2011)
  • Author(s): Konno, Y.
  • Organizer: September 5 -17. 2011 Hammamet,TUNISIA
  • Year and Date: 2011-09-07
• [Presentation] Shrinkage estimation of a mean matrix of a multivariate complex normal distribution (2010)
  • Author(s): Y.Konno
  • Organizer: 研究集会「統計的推測方法の理論的展開とその応用」
  • Place of Presentation: 熊本大学自然科学研究科
  • Year and Date: 2010-11-17
• [Remarks]
  • URL: http://mcm-www.jwu.ac.jp/~konno/resarch.html
• [Remarks] List of Papers
  • URL: http://mcm-www.jwu.ac.jp/~konno/list.html
• [Remarks]
  • URL: http://mcm-www.jwu.ac.jp/~konno/resarch.html
• [Remarks]
  • URL: http://mcm-www.jwu.ac.jp/~konno/resarch.html
• [Remarks]
  • URL: http://mp-w3math.jwu.ac.jp/~konno/resarch.html