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1993 Fiscal Year Final Research Report Summary

Basic Models for Statistical Multiple Comparisons and its applications

Research Project

Project/Area Number 04630018
Research Category

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

Allocation TypeSingle-year Grants
Research Field Economic statistics
Research InstitutionMeisei University

Principal Investigator

SIOTANI Minoru  Meisei University, General Education, Professor, 一般教育, 教授 (50116597)

Co-Investigator(Kenkyū-buntansha) UKITA Yoshimasa  Meisei University, Science and Engineering, Professor, 理工学部, 教授 (70168673)
Project Period (FY) 1992 – 1993
KeywordsElliptically population / Multiple comparison / T^2_-type statistics / Modified second approximation method / Structure covariance matrix of error term / Decomposition of overall hypotheses / Meanings of formal deducted hypotheses / Cyclic random vector
Research Abstract

1. For the Results related to Multivariate Analysis :
(1) The first stage fundamentals for the sampling theory under a elliptical population : When the population is ellipitical, sample mean x^^- and sample covariance matrix S are not necessarily independent, which is different from the Normal case. This causes the difficulties in the analysis. Overcoming of these difficulties is essential in the development of the theory.In the research, formulas for obtaining the limiting distribution of functions of S, f(S) and asymptotic expansion for E[f(S)] are given. The concrete example are given. The research may promise further fruits for the multiple comparisons.
(2) In the normal case, the modified second approximation method for evaluating the upper percentiles of T^2_-type statistics is examined by large scale of Monte Carlo numerical experiments. This is done concretely for the multidimensional range and for the statistics defined for comparing several trial treatments with a control treat … More ment. Also effective range of parameters sufficient for the parctical use is determined.
2. For the Results of Experimental Designs and Analysis of Variance :
Convariance matrix SIGMA in the general linear model x - N_p(R_Xl_p + mu, SIGMA ) is of some specific structure. Under this structure of SIGMA, the sample space is decomposed, with respect to SIGMA, into latent subspaces corresponding to distinct latent roots. Correspondingly the overall hypothesis that all components of mu are equal is decomposed into sets of subhypotheses of multiple contrasts c_i'mu = 0, i=1, 2, ..., r. And F-statistics corresponding to subhypothese are defined. However it should be checked, in this mathematical formation, whether or not the setted subhypotheses have practical meanings. In this project, cases of split plot design, repeated observations, and cyclic random vector are investigated concretely. Fortunately, in these special cases, reducted subhypotheses have practical meaning when the dimensionaliy is lower values (p=1, 2, ..., 5). Finally these test procedures are compared with the well known Hotelling's T^2-test procedure with respect to effectiveness. Less

  • Research Products

    (14 results)

All Other

All Publications (14 results)

  • [Publications] Takashi Seo: "Multivariate Studentized range and its upper percentiles" Journal of Japan Statistical Society. 22. 123-137 (1992)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Takashi Seo: "Approximation to the upper percentiles of T^2_<max>-type statistics" Statistical Sciences and Data Analysis(K.Matusita,M.L.Puri and T.Hayakawa eds.). VSP. 265-276 (1993)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Minoru Siotani: "Some aspects of my experience of statistical research regarded as useful even today" Journal of Japan Statistical Society. 23. 115-121 (1993)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Toshiya Iwashita: "Asymptotic distributions of functions of a sample covariance matrix under the elliptical distribution" Canadian Journal of Statistics. 22(in print). (1994)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 宇喜多義昌: "Generalized Linear Modelをもつ2要因2水準の要因実験で,反復実験の場合の統計的仮説検定問題について" 明星大学研究紀要-理工学部-. 28. 1-12 (1992)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 宇喜多義昌: "Cyclic Random Vector xの母平均μの多重比較H:c^′_iμ=0(i=1,2,...,l)に関するUMP-Testについて" 明星大学研究紀要-理工学部-. 29. 1-13 (1993)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 宇喜多義昌: "Random Vector xの母平均Vector μの多重比較c^′_iμ=0(i=1,2,...,r)の2つの検定方式の有効性の比較" 明星大学研究紀要-理工学部-. 30. 1-13 (1994)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Takashi Seo: "Multivariate Studentized range and its upper percentiles" Jour.Japan Statist.Soc.Vol.22. 123-137 (1992)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Takashi Seo: "Approximation to the upper percentiles of T^2_-type statistics" Statistical Sciences and Data Analysis (Matusita et al.eds). VSP. 265-276 (1993)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Minoru Siotani: "Some aspects of my experience of statistical research regarded as useful even today" Jour.Japan Statist.Soc.Vol.23. 115-121 (1993)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] T.Iwashita: "Asymptotic distributions of functions of a sample convariance matrix unde the elliptical distribution" Canadian Journal of Statistics. Vol.22(in print). (1994)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Yoshimasa Ukita: "Problems of statistical testing hypothesis in the case of 2 factors-2levels factorial experiment with general linear model-repeated observations-" Research Papers of Meisei University (Faculty of Science and Engineering). Vol.28. 1-12 (1992)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Yoshimasa Ukita: "UMP-Test for the multiple comparisons H : c_i'mu = 0 (i=1, 2, ..., ) on the population mean mu of cyclic random vector x" Research Papers of Meisei University (Faculty of Science and Engineering). Vol.29. 1-13

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Yoshimasa Ukita: "Effectiveness comparison of 2 test procedures of multiple comparisons c_i'mu (i=1, 2, ..., r) on the population mean mu of random vector x" Research Papers of Meisei University (Faculty of Science and Engineering). Vol.30. 1-13

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

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Published: 1995-03-27  

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