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1994 Fiscal Year Final Research Report Summary

A study of statistical inference in multivariate nonnormal models

Research Project

Project/Area Number 05452014
Research Category

Grant-in-Aid for General Scientific Research (B)

Allocation TypeSingle-year Grants
Research Field General mathematics (including Probability theory/Statistical mathematics)
Research InstitutionHIROSHIMA,UNIVERSITY

Principal Investigator

FUJIKOSHI Yasunoro  Hiroshima Univ., Mathematics, Professor, 理学部, 教授 (40033849)

Co-Investigator(Kenkyū-buntansha) TAKENAKA Shigeo  Hiroshima Univ., Associate Professor, 理学部, 助教授 (80022680)
KUBO Izumi  Hiroshima Univ., Professor, 理学部, 教授 (70022621)
WATAMORI Yoko  Hiroshima Univ., Research Assistant, 理学部, 助手 (70240538)
FUJIOKA Teruo  Hiroshima Univ., Research Assistant, 理学部, 助手 (50221544)
SASABUCHI Syoichi  Hiroshima Univ., Mathematics, Associate Professor, 理学部, 助教授 (20128028)
Project Period (FY) 1993 – 1994
KeywordsMultivariate nonnormal models / Statistical inference / Multivariate analusis of variance / Canonical correlation model / Lagevin distribution / Inequality restriction / Semi-parametric regression model / Robustness
Research Abstract

Research results of this projects can be divided roughly into the following three categories :
1. First, to study how effective the statistical procedures proposed under multivariate normal models are under multivariate nonnormal models, and next, to develop the statistical procedures applicable for more general situations.
2. To develop the statistical procedures in some speficic multivariate nonnormal models.
3. Research on related topics in statistic and mathematics.
Related to the first category, Y.Fujikoshi studied on some multivariate test statistics and latent roots in multivariate analysis of variance, and aucceeded to obtain some new results under elliptical distributions and a general distribution involving continuous distributions.
Related to the second category, Y.Watamori developed higher order asymptotic theory of statistical inference on Langevin distribution, and explored instrinsic approach of statistical distributions on a sphere. S.Sasabuchi made a comparative study of several tests for the equality of several binomial populations with ordered restrictions. T.Fujioka gave an exiplicite expression for the estimator of variance based on minimax approach in semi-parametric regression model, and studied its properties.
Related to the third category, we obtained new results on various areas : Y.Fujikoshi 「statistical inference of repeated measurements and its applications and error bounds for asymptotic expansions of distributions」 , S.Sasabuchi 「statistical inference of multivariate normal distributions with ordered restrictions」 , I.Kubo, S.Takenaka and M.Nakamura 「probability Theory」 , T.Kusano, M.Mimura and M.Naito 「Analysis」 , A.Kowata 「Geometry」 .

  • Research Products

    (24 results)

All Other

All Publications (24 results)

  • [Publications] Takahisa Yokoyama: "A parallel profile model with random-effects covariance structure" Journal of Japan Statistical Society. 23. 83-89 (1993)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Yasunori Fujikoshi: "Recent developments and perspectives in multivariate analysis" Journal of Japan Statistical Society. 22. 313-356 (1993)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Takashi Seo: "The effects on the distributions of sample canonical correlations under nonnormality" Communication in Statistics:Theory and Method. 23. 2615-2628 (1994)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Takashi Seo: "Asymptotic distributions of the sample roots in MANOVA models under nonnormality" Journal of Japan Statistical Society. 24. 133-140 (1994)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Takashi Seo: "The effects of nonnormality on tests for dimensionality in canonical correlation and MANOVA models" Journal of Multivariate Analysis. 52. 325-337 (1995)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Syoichi Sasabuchi: "不等式制約の下での統計的推測" 数学. 45. 42-54 (1993)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Teruo Fujioka: "The max-MSE's of minimax estimators of variance in nonparametric regression" Hiroshima Mathematical Journal. 24. 573-581 (1994)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Yoko Watamori: "Statistical inference of Langevin distribution for directional data" Hiroshima Mathematical Journal. (掲載予定).

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Izumi Kubo: "The structure of Hida distributions" Mathematical Approach to Fluctuations I,World Scientific. 49-114 (1994)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Shigeo Takenaka: "Examples of self-similar stable processes" Stochastic Processes,A Festschrift in Honour of Gopinath Kallianpur,Springer. 303-311 (1993)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Manabu Naito: "Solutions with prescribed numbers of zeros for nonlinear second order differential equations" Funkcialaj Ekvacioj. 37. 505-520 (1994)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Atsutaka Kowata: "On the irreducible components of the solutions of Matsuo's differential equations" Hiroshima Mathematical Journal. (掲載予定).

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Takahisa Yokoyama: "A parallel profile model with random-effects covariance sturucture" Journal of Japan Statistical Society. 23. 83-89 (1993)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Yasunori, Fujikoshi: "Recent developments and perspectives in multivariat analysis" Journal of Japan Statistical Society. 22. 313-356 (1993)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Takashi Seo: "The effects on the distributions of sample canonical correlations under nonnormality" Communication in Statistics : Theory and Method. 23. 2615-2628 (1994)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Takashi Seo: "Asymptotic distributions of the sample roots in MANOVA models under nonnormality" Journal of Japan Statistical Society. 24. 133-140 (1994)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Takashi Seo: "The effects of nonnormality on tests for dimensionality in canonical correlation and MANOVA models" Journal of Multivariate Analysis. 52. 325-337 (1995)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Syoichi Sasabuchi: "Statical inference under inequality restrictions" to appear in Sugaku Expositions.

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Teruo Fujioka: "The max-MSE's of minimax estimators of variance in nonparametric regression" Hiroshima Mathematical Journal. 24. 573-581 (1994)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Yoko Watamori: "Statistical inference of Langevin distribution for directional data" to appear in Hiroshima Mathematical Journal.

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Izumi Kubo: "The structure of Hida distributions" Mathematical Approach to Fluctuations I,World Scientific. 49-114 (1994)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Shigeo Takenaka: "Examples of self-similar stable processes" Stochastic Processes, A Festschrift in Honor of Gopinath Kallianpur. Springer. 303-311 (1993)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Manabu Naito: "Solutions with prescribed numbers of zeros for nonlinear second oeder differential equations" Funkcialaj Ekvacioj. 37. 505-520 (1994)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Atsutaka Kowata: "On the irreducuble components of the solution of Matsuo's differential equations" to appear in Hiroshima Mathematical Journal.

    • Description
      「研究成果報告書概要(欧文)」より

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Published: 1996-04-15  

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