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Relation of the precision of asymptotic expoansions with sample sizes and dimensionality in statistical inference

Research Project

Project/Area Number 06680293
Research Category

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

Allocation TypeSingle-year Grants
Research Field Statistical science
Research InstitutionMeisi University

Principal Investigator

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

Co-Investigator(Kenkyū-buntansha) IWASHITA Toshiya  Science University of Tokyo, Department of Management Sciences, ASssistant Profe, 工学部, 助手 (20266919)
HIRAKAWA Kozaburo  Meisei University, General Education, Professor, 一般教育, 教授 (80084367)
UKITA Yoshimasa  Meisei University, General Education, Professor, 一般教育, 教授 (70168673)
Project Period (FY) 1994 – 1995
Project Status Completed (Fiscal Year 1995)
Budget Amount *help
¥2,000,000 (Direct Cost: ¥2,000,000)
Fiscal Year 1995: ¥1,100,000 (Direct Cost: ¥1,100,000)
Fiscal Year 1994: ¥900,000 (Direct Cost: ¥900,000)
Keywordsprecision of asymptotic expansion for mula / Hotelling's T^2-test / experimental approximate upper bound / Precision and sample size / OC function and curve / construction method of upper bound / elliptical population / covariance matrix structure / comparison of tests / 回帰係数に対する仮説検定 / 漸近展開近似の精度と標本 / HotellingのT^2-検定のOC関数 / 回帰分析 / 最小二乗法 / 数値実験による実験公式 / 楕円型母集団のもとでの漸近展開 / 分散構造に基づく検定法の比較
Research Abstract

In mulotivariate statistical analysis, the inference procedures are often based on asymptotic expansions for the distributions of key statistics in the underlying inferences. the aim of this research is to search an effective method applicable for the general problem of studying the practical validity of asymptotic expansion formulae used in the statistical inference. In oder to investigate the problem concretely, the asymptotic expansion formula for the OC function of Hotelling's T^2-test was considered.
The OC function depends on the dimensionality p, samplle siza n and noncentrality parameter DELTA. An experimental formula of the approximate upper bound on the absolute error Y of the asymptotic expansion formula for the OC function was obtained, which is a function of p, n and DELTA, that is,
Y<less than or equal>U=0.45702 P^<0.28736> N^<-1.04252>exp{-154232(DELTA-0.39981)}, N=n-p (*)
in D, the reference domain of p, n, DELTA, which was determined concretely. The practical effectivenes … More s of this upper bound U was cheked over prameter sets in D.The formula (*)is used to obtain the method of determining a sample size with which a certain requirement on Y or on test. This shows that the construction method of the upper bound on Y is useful and moreover is hopeful to extend its use to other cases ; actually the investigation on the probability of misdiscrimination in the discriminant analysis is now in progress by the similar method.
The results obtained by this research were reported in the annual meetin of Japan statistical Society and Japan-American Joint Meeting on Multivariate Staristical Inference 2000, and the paper will be published in American Journal of Mathematical and Management Sciences.
AS preliminary works on the research project, some results on the T^2 -distribution when the underlying pupulation distribution is elliptical, and on test statistics for testing some multiple comparison hypotheses when the coveriance matrix structure is specific depending on the underlying experimental design. Less

Report

(3 results)
  • 1995 Annual Research Report   Final Research Report Summary
  • 1994 Annual Research Report
  • Research Products

    (18 results)

All Other

All Publications (18 results)

  • [Publications] 宇喜多義昌: "Random Vecton xの母平均Vecton μの多重比較 c′iμ=O(i=l,…,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
    • Related Report
      1995 Final Research Report Summary
  • [Publications] 宇喜多義昌: "Random Vecton xの母平均Vecton μの多重比較 c′iμ=O(i=l,…,r)の2つの検定方式の有効性の比較,Part II" 明星大学研究紀要-理工学部-. 31. 1-7 (1995)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] 塩谷実: "統計的推測における漸近展開公式の精度に対する実験的上限の構成-T^2-検定を素材にして構成法を探る-" 明星大学情報学部紀要. 4(受理). (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] Minoru SIOTANI: "Asymptotic expansion for sampling distribution and sample size in statistical inference -Presentation of the pro blem,illustrated by the T^2-test (Accepted)" American Journal of Mathematical and Management Sciences ; Special volume : Multivariate Statistical Inference 2000. (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] Toshiya IWASHITA: "Adjustment of Bartlett type to Hotelling's T^2-statistic under the elliptical distribution (Accepted)" American Journal of Mathematical and Management Sciences ; Special volume : Multivariate Statistical Inference 2000. (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] 宇喜多義昌: "Gemeral Linear Modelの場合の回帰係数に関する仮説検定の研究" 明星大学研究紀要-理工学部-. 32. 1-8 (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] UKITA, Yoshimasa: "Effectiveness comparison of 2 test procedures for multiple comparisons c! mu=0 (i=1, .., r) on the population mean mu of random vector x" Reserch Memoir of Meisei University (Faculty of Science and Engineering). Vol.30. 1-13 (1994)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] UKITA, 1Yoshimasa: "Effectiveness comparison of 2 test procedures for multiple comparisons c! =0(i=1, .., r) on the population mean mu of random vector x, Part II." Research Memoir of Meisei University (Faculty of Science and Engineerign). Vol. 31. 1-7 (1995)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] SIOTANI, Minoru: "Construction of an experimental upper bound on the precision of asymptotic expansion formula in the statistical inferences. -Search of a construction method based on T^2 -test." Research Memoir of Meisei University (Faculty of Information). Vol.4 (Accepted). (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] SIOTANI, Minoru: "Asymptotic expansion for sampling distribution and sample size in statistical inference-Presentation of the problem, illustrated by the T^2-test." American Journal of Mathematical and Management Sciences ; Special Volume on Multivariate Statistical Inference 2000. (Accepted). (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] IWASHITA, Toshiya: "Adjustment of Bartlett type to Hotelling's T^2-statistic under the elliptical distribution." American Journal of Mathematical and Management Sciences ; Special Volume on Multivariate Statistical Inference 2000. (Accepted). (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] UKITA, Yoshimasa: "Testing hypotheses for on reression coefficients in the case of general linear model." Research Memoir of Meisei University (Faculty of Science and Engineering). Vol. 32. 1-8 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] "統計的推測における漸近展開公式の精度に対する実験的上限の構成" 明星大学情報学部紀要. 4(受理). (1996)

    • Related Report
      1995 Annual Research Report
  • [Publications] "General Linear Modelの場合の回帰係数に関する仮説検定の研究" 明星大学研究紀要-理工学部. 32. 1-8 (1996)

    • Related Report
      1995 Annual Research Report
  • [Publications] M. Siotani, T. Iwashita and T. Seo: "Asymptotic expansion for sampling distribution and sample size in statistical inferenence I-Presentation of the problem (受理)" American Journal of Mathematical and Management Sciences (Special Volume: Multiv. Analy. Stat. Inf.). 5. (1996)

    • Related Report
      1995 Annual Research Report
  • [Publications] T. Iwashita: "Adjusutment of Bartlett type to Hotelling's T^2-statistic under the elliptical distribution (受理)" American Journal of Mathematical and Management Sciences (Special Volume: Multiv. Analy. Stat. Inf.). 5. (1996)

    • Related Report
      1995 Annual Research Report
  • [Publications] Toshiya IWASHITA: "Adjustment of Bartlett Type to Hotelling´s T^2-Statistic under the Elliptical Distribution" American Journal of Mathematical and Management Sciences:Volume in honor of Prof.M.Siotani. (1995)

    • Related Report
      1994 Annual Research Report
  • [Publications] 宇喜多 義昌: "Random Vector xの母平均Vector uの多重比較方式の有効性の比較;PartII C_iu=0(i=1,・・・,r)の2つの検定" 明星大学研究紀要-理工学部-. 31. 1-12 (1995)

    • Related Report
      1994 Annual Research Report

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Published: 1994-04-01   Modified: 2016-04-21  

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