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Error Bounds for Asymptotic Expansions and Approximation of Probability Distributions

Research Project

Project/Area Number 62540173
Research Category

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

Allocation TypeSingle-year Grants
Research Field General mathematics (including Probability theory/Statistical mathematics)
Research InstitutionThe Institute of Statistical Mathematics

Principal Investigator

SHIMIZU Ryoichi  The Institute of Statistical Mathematics, Professor, 統計基研究系, 教授 (10000192)

Co-Investigator(Kenkyū-buntansha) AKI Shigeo  The Institute of Statistical Mathematics, Assistant Professor, 統計基礎研究系, 助手 (90132696)
KONISHI Sadanori  The Institute of Statistical Mathematics, Associate Professor, 統計基礎研究系, 助教授 (40090550)
HIRANO Katsuomi  The Institute of Statistical Mathematics, Associate Professor, 統計教育情報センター, 助教授 (30000186)
Project Period (FY) 1987 – 1988
Project Status Completed (Fiscal Year 1988)
Budget Amount *help
¥800,000 (Direct Cost: ¥800,000)
Fiscal Year 1988: ¥400,000 (Direct Cost: ¥400,000)
Fiscal Year 1987: ¥400,000 (Direct Cost: ¥400,000)
KeywordsAsymptotic expansion / Limiting distributions / Fvaluation of errors / Normal distribution / 推定 / 極限定理 / 確率分布 / 近似 / 逆ガウス分布 / ウィーナー過程
Research Abstract

In the theory of sampling distributions we often encounter with the situation who distribution of a statistic can not be obtained in a closed from, or even if it is obtain distribution is of no use because of its complexity. Therefore, studies on approximation distributions become important.
Limiting forms of the sampling distributions, which are relatively simple, have been c wide class of statistics. Much has also been done about the expansion of the sampling distril its limiting distribution. However, from the practical, as well as theoretical, point of important problem in approximating a probability distribution by some sort of functions is accuracy of the approximation, i.e., to evaluate an upper bound of the error of the approxim
In this research project we investigated asymptotic expansions of the density of the dis a random variable of the form Y=sigmaX, where epsilon(>0) and X are independent and X follows normal distribution N(0,1), assuming implicitly, that sigma is close 1 in the sense that both E E(sigma^<-2>- 1)^k are small. The expansion is given in terms of E(sigma^<+2>- 1)^j,j = 0,1,...,k-1,polynomials, and the difference between f and its approximation is absolutely integrable o space and is bounded by, roughly speaking, constant times the sum of E(sigma^2- 1)^k and E( particular, the probability of the event YepsilonA is approximated, within this error, by the in approximating function over the set A. The result is expected to be applicable to the multivar
Another result of our research includes determination of the limit distribution of some test

Report

(3 results)
  • 1988 Annual Research Report   Final Research Report Summary
  • 1987 Annual Research Report
  • Research Products

    (22 results)

All Other

All Publications (22 results)

  • [Publications] 藤越康祝,清水良一: 数学(日本数学会々誌). 40. 202-236 (1988)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] SHIMIZU Ryoichi: Journal of Statistical Planning and Inference. 21. 305-314 (1989)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] KONISHI Sadanori.GUPTA A.P.: Journal of Statistical Planning and Inference. 21. 93-105 (1988)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] AKI Shigeo.;KASHIWAGI N.: Research Memorandum,The Inst.Statist.Math.352.

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] AKI Shigeo,;HIRANO Katsuomi: Annals of Inst. Statist.Math.41. 47-61 (1989)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] HIRANO Katsuomi,;IWASE K.: Communication in Statistics-Theory and Methods. 18. 189-197 (1989)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] FUJIKOSHI,Y.; SHIMIZU,Ryoichi: "Asymptotic expansions of some distributions and their error bounds (in Japanses. to be translated into English by American Mathematical Society)" Sugaku(Mathematics) - Journal of Mathematical Society of Japan. 40. 202-236 (1988)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] SHIMIZU,Ryoichi: "Expansion of scale mixtures of the gamma distribution" Journal of Statistical Planning and Inference. 21. 305-314 (1989)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] KONISHI,Sadanori; GUPTA A.P.: "Testing the equality of several intraclass correlation coefficient" Journal of Statistical Planning and Inference. 21. 93-105 (1988)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] AKI,Shigeo; HIRANO,Katsuomi: "Estimation of parameters in the discrete distributions of order k" Annals of the Institute of Statistical Mathematics. 41. 47-61 (1989)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] AKI,Shigeo; KASHIWAGI,N.: "Asymptotic properties of some goodness-of-fit tests based on th L_l-norm" Research Memorandum, Institute of Statistical Mathematics,. 352.

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] 清水良一: 研究報告書に収めたものを整理加筆して英文誌に.

    • Related Report
      1988 Annual Research Report
  • [Publications] KONISHI,Sadanori.; GUPTA,A.K.: Journal of Sratistical Planning and Inference. 21. 93-105 (1988)

    • Related Report
      1988 Annual Research Report
  • [Publications] SHIMIZU,Ryoichi.: Journal of Statistical Planning and Inference. 21. 305-314 (1989)

    • Related Report
      1988 Annual Research Report
  • [Publications] AKI,Shigeo.; KASHIWAGI,N.: Research Memorandum,Institute of Statistical Mathematics. 352.

    • Related Report
      1988 Annual Research Report
  • [Publications] AKI,Shigeo.; HIRANO,Katsuomi: Annals of Institute of Statistical Mathematics. 41. 47-61 (1989)

    • Related Report
      1988 Annual Research Report
  • [Publications] HIRANO,Katsuomi.; IWASE,K.: Research Memorandum,Institute of Statistical Mathematics. 354.

    • Related Report
      1988 Annual Research Report
  • [Publications] 藤越康祝,清水良一: 数学(日本数学会編). 40. (1988)

    • Related Report
      1987 Annual Research Report
  • [Publications] Shimizu, Ryoichi: To appear in Journal of statistical planning and inference.(1988)

    • Related Report
      1987 Annual Research Report
  • [Publications] Konishi, Sadanori: To appear in Annals of the institute of statistical mathematics.40. (1988)

    • Related Report
      1987 Annual Research Report
  • [Publications] Hirano, Katsuomi, Aki, Sigeo: Statistics and Probabilty Letters. 6. 67-69 (1987)

    • Related Report
      1987 Annual Research Report
  • [Publications] Hirano, Katsuomi, Iwase, Kosei: Research Memorandum. NO.348. (1988)

    • Related Report
      1987 Annual Research Report

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Published: 1987-04-01   Modified: 2016-04-21  

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