Analysis of Multivariate Distribution from a new standpoint

• Project/Area Number: 19530181
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Economic statistics
• Research Institution: Shinshu University
• Principal Investigator: SHIINA Yo Shinshu University, 経済学部, 教授 (80242709); SHIINA Yo (2009) Shinshu University, 経済学部, 教授 (84202709)
• Project Period (FY): 2007 – 2010
• Project Status: Completed (Fiscal Year 2010)
• Budget Amount: ¥2,600,000 (Direct Cost: ¥2,000,000、Indirect Cost: ¥600,000); Fiscal Year 2010: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000); Fiscal Year 2009: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000); Fiscal Year 2008: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000); Fiscal Year 2007: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
• Keywords: 多変量正規分布 / ウィシャート分布 / 楕円分布 / 分散共分散行列 / 固有根 / 許容的 / 情報幾何 / 計量経済学 / リーマン幾何学 / AR(1) / 多変量分布 / ベクトル空間 / 微分幾何 / リーマン計量 / 多変量解析

Research Abstract

On multivariate distributions, we have got following results ; 1) For Wishart distributions, we derived the distribution of the sample eigenvalues and eigenvectors when population eigenvalues are block-wise infinitely dispersed. 2) For multivariate normal distributions, we derived an admissible estimator of population eigenvalues with respect to a normalized quadratic loss function. 3) For elliptically contoured distributions, we improved the classical estimator of the population contribution rates.

Research Products

• [Journal Article] Modified estimator of the contribution rates of population eigenvalues (2011)
  • Author(s): Yo Sheena
  • Journal Title: arXiv 1104 Pages: 1019-1019
• [Journal Article] Admissible estimator of the eigenvalues of the variance-covariance matrix for multivariate normal distributions (2011)
  • Author(s): Yo Sheena, A.Takemura
  • Journal Title: Journal of Multivariate Analysis Vol.102 Pages: 801-815
  • Peer Reviewed
• [Journal Article] Asymptotic Distribution of Wishart Matrix for Block-wise Dispersion of Population Eigenvalues (2008)
  • Author(s): Yo Sheena, A.Takemura
  • Journal Title: Journal of Multivariate Analysis Vol.99 Pages: 751-775
  • Peer Reviewed
• [Journal Article] Asymptotic distribution of Wishart matrix for block-wise dispersion of population eigenvalues (2008)
  • Author(s): Yo Sheena, Akimichi Takemura
  • Journal Title: J.Multi.A. 99(4) Pages: 751-775
  • Peer Reviewed
• [Journal Article] Asymptotic distribution of Wishart matrix for block-wise dispersion ofpopulation eigenvalues (2008)
  • Author(s): Yo Sheena, Akimichi Takemura
  • Journal Title: Journal of multivariate analysis 99 Pages: 751-775
  • Peer Reviewed
• [Journal Article] An asymptotic expansion of Wishart distribution when the population eigenvalues are infinitely dispersed (2007)
  • Author(s): Yo Sheena, Akimichi Takemura
  • Journal Title: Statistical Methodology 4(2) Pages: 158-184
  • Peer Reviewed
• [Journal Article] An asymptotic expansion of Wishart distribution when the population eigenvalues are infinitely dispersed (2007)
  • Author(s): Yo Sheena and Akimichi Takemura
  • Journal Title: Statistical Methodology 4 Pages: 158-184
  • Peer Reviewed
• [Journal Article] Admissible Estimator of the Eigenvalues of Variance-Covariance Matrix for Multivariate Normal Distributions
  • Author(s): Yo Sheena, Akimichi Takemura
  • Journal Title: Journal of Multivariate Analysis Volume: (近刊予定)
  • Peer Reviewed
• [Presentation] Admissible Estimator of the Eigenvalues of Variance-Covariance Matrix for Multivariate Normal Distributions (2010)
  • Author(s): Yo Sheena
  • Organizer: The 7th conference on multivariate distributions with applications
  • Place of Presentation: Maresias, Brazil
  • Year and Date: 2010-08-11
• [Presentation] Admissible estimator of the eigenvalues of the variance-covariance matrix for multivariate normal distributions (2010)
  • Author(s): Yo Sheena
  • Organizer: The 7th conference on multivariate distributions with applications
  • Place of Presentation: Maresias, Brazil