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Research on Test and Estimate of Distribution Function and its Functionals

Research Project

Project/Area Number 03630014
Research Category

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

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

Principal Investigator

SHIRAHATA Shingo  Osaka University, College of General Education Professor, 教養部, 教授 (10037294)

Co-Investigator(Kenkyū-buntansha) CHU In-sun  Osaka University, Faculty of Engineering Science, Research Assistant, 基礎工学部, 助手 (50243192)
AKI Shigeo  Osaka University, Faculty of Engineering Science, Associate Professor, 基礎工学部, 助教授 (90132696)
TANIGUCHI Masanobu  Osaka University, Faculty of Engineering Science, Associate Professor, 基礎工学部, 助教授 (00116625)
ISOGAI Takafumi  Osaka University, College of General Education Associate Professor, 教養部, 助教授 (00109860)
Project Period (FY) 1991 – 1992
Project Status Completed (Fiscal Year 1992)
Budget Amount *help
¥1,500,000 (Direct Cost: ¥1,500,000)
Fiscal Year 1992: ¥600,000 (Direct Cost: ¥600,000)
Fiscal Year 1991: ¥900,000 (Direct Cost: ¥900,000)
KeywordsDistribution Function / Empirical Distribution / Kernel Estimate / Goodness of Fit Test / Estimate / Confidence Band / Bootstrap / Mean Integrated Square Error / 核関数 / U-統計量 / 検定 / ブ-ツトラップ
Research Abstract

Distribution function and its functionals play important roles in statistical inferences. In parametric frame works, the likelihood is represented by density functions. In nonparametric theory, several hypotheses are given by distribution functions. The aim of this research project is to develop theory and method on test and estimate of distribution function and its functionals. The head investigator and the investigators singly or jointly obtained the following results.
1. In the estimate of distribution function, the kernel estimators are better than the empirical distribution function in the sense of integrated mean squared error. In our work, the superiority of the kernel estimator is shown to be not true in the sense of integrated squared error. Hence, we recommend to use kernel estimator if we adhere the continuity, and to use empirical distribution function if otherwise. 2. We must give the smoothing parameter in the kernel estimators. In order to select the parameter, we must estimate the errors. It is shown that the bootstrap method is very useful in the estimate of the errors. 3. The usual confidence band of distribution function is based on the supremum of the absolute deviation. However, the band is not accurate for extreme points. A new confidence band is given in order to recover the defect of the usual method. 4. Goodness of fit tests based on graphical representation of data and a characterization of distribut ions are proposed. 5. The second order and the third order efficiency of statistics in time series and non-linear regression models are derived. 6. Some extensions of binomial distribution of order k and negative binomial distribution of order k are considered. Moment generating functions and variances of waiting time occurred in two-state Markov chain are derived.

Report

(3 results)
  • 1992 Annual Research Report   Final Research Report Summary
  • 1991 Annual Research Report
  • Research Products

    (38 results)

All Other

All Publications (38 results)

  • [Publications] SHIRAHATA,S.(SHIRAHATA,S.): "Contidence band tor distribution function" Studies Humanity and Social Science. 40. 105-110 (1991)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1992 Final Research Report Summary
  • [Publications] SHIRAHATA,S.(SHIRAHATA,S.): "Integrated squared error of kernel-type estrmator of distribution tunction" Annals of Institute of Statistical Mathematics. 44. 579-591 (1992)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1992 Final Research Report Summary
  • [Publications] SHIRAHATA,S.(SHIRAHATA,S.): "Estimate of variance of U-statistics" Communications in Statistics;Theory&Methods. 21. 2969-2981 (1992)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1992 Final Research Report Summary
  • [Publications] ISOGAI,T.(ISOGAI,T.): "Some measurement models velated to an inverse Gaussian distribution" Reports of Statistical Application Research. 36. 1-11 (1991)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1992 Final Research Report Summary
  • [Publications] AKI,S.(AKI,S.): "Waiting time Problems for a sequence of discrete random varicbles" Annals of Institute of Statrstical Mathematics. 44. 363-378 (1992)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1992 Final Research Report Summary
  • [Publications] Chu,I.-S.(Chu,I.-S.): "Bootstrap selection of smoothing parameter for distribution function estination" Mathematica Japonica. 38. (1993)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1992 Final Research Report Summary
  • [Publications] TANIGUCHI,M.(TANIGUCHI,M.): "Higher order asymptotic theory for time series analysis" Springer-Verlag, VIII+160 (1991)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1992 Final Research Report Summary
  • [Publications] Shirahata, S. (Chu, I. -S.): "Law of the iterated logarithm for two-sample empirical process and Chernoff-Savage statistics" J. Japan Statist. Soc. 21. 85-95 (1991)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1992 Final Research Report Summary
  • [Publications] Shirahata, S. (Shirahata, S.): "Confidence band for distribution function" Studies Humanity Social Sci. 40. 105-110 (1991)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1992 Final Research Report Summary
  • [Publications] Shirahata, S. (Shirahata, S.): "Integrated squared error of kernel-type estimator of distribution function" Ann. Inst. Statist. Math. 44. 579-591 (1992)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1992 Final Research Report Summary
  • [Publications] Shirahata, S. (Shirahata, S.): "Estimates of variance of U-statistics" Commun. Statist. 21. 2969-2981 (1992)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1992 Final Research Report Summary
  • [Publications] Shirahata, S. (Shirahata, S.): "Linked line chart and induced test statistics. (in Japanese)" Bull. Compu. Statist. Japan. 5. 45-57 (1992)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1992 Final Research Report Summary
  • [Publications] Shirahata, S. (Goto, M.): "Recent development of statistical graphics. (in Japanese)" J. Japan Statist. Soc. 21. 333-351 (1992)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1992 Final Research Report Summary
  • [Publications] Isogai, T. (Isogai, T.): "Some measurement models related to an inverse Gaussian distribution" Rep. Statist. Appl. Res., JUSE. 36. 1-11 (1991)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1992 Final Research Report Summary
  • [Publications] Isogai, T. (Hiratsuka, A.): "Study on sludge dewatering techniques using a statistical model-in view of both quantity of filtrate and filtrate quality" Res. Env. System. 20. 231-241 (1992)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1992 Final Research Report Summary
  • [Publications] Taniguchi, M. (Taniguchi, M.): "Higher Order Asymptotic Theory for Time Series Analysis" Lec. Note Statist. 68, Springer. (1991)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1992 Final Research Report Summary
  • [Publications] Taniguchi, M. (Taniguchi, M.): "Third-order asymptotic properties of a class of test statistics under a local alternative" J. Multivariate Anal. 37. 223-238 (1991)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1992 Final Research Report Summary
  • [Publications] Taniguchi, M. (Hosoya, Y.): "Higher-order asymptotic theory of time-series analysis" Sugaku Expositions. 4. 223-249 (1991)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1992 Final Research Report Summary
  • [Publications] Taniguchi, M. (Taniguchi, M.): "An automatic formula for the second-order approximation of the distributions of test statistics under contiguous alternatives" Inter. Statist. Review. 60. 211-225 (1992)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1992 Final Research Report Summary
  • [Publications] Taniguchi, M. (Taniguchi, M.): "Non-parametric approach in time series analysis" J. Time Series Anal. (1993)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1992 Final Research Report Summary
  • [Publications] Taniguchi, M. (Kondo, M.): "Two sample problem in time series analysis" Proc. 3rd Pacific Area Statist. Conf. (1993)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1992 Final Research Report Summary
  • [Publications] Aki, S. (Hirano, K.): "On Ling's binomial and negative binomial distributions of order k" Statist. Prob. Letters. 11. 503-509 (1991)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1992 Final Research Report Summary
  • [Publications] Aki, S. (Aki, S.): "Waiting time problems for a sequence of discrete random variables" Ann. Inst. Statist. Math. 44. 363-378 (1992)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1992 Final Research Report Summary
  • [Publications] Aki, S. (Hirano, K.): "On number of occurrences of success runs of specified length in a two-state Markov chain" Statist. Sinica. (1993)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1992 Final Research Report Summary
  • [Publications] Aki, S. (Aki, S.): "Discrete distributions related to succession events in a two-state Markov chain" Statist. Sci. Data Anal. Int. Sci. Pub. Zeist. (1993)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1992 Final Research Report Summary
  • [Publications] Chu, I. -S. (Chu, I. -S.): "Bootstrap selection of smoothing parameter for distribution function estimation" Math. Japo. (1993)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1992 Final Research Report Summary
  • [Publications] 白旗 慎吾(白旗 慎吾): "連結線分図とそれに基づく検定統計量" 計算機統計学. 5. 45-57 (1992)

    • Related Report
      1992 Annual Research Report
  • [Publications] Shirahata,S.(Shirahata,S.): "Integrated squared error of kernel-type estimator of distribution tunction" Annals of Institnte of Statistical Mathematics. 44. 579-591 (1992)

    • Related Report
      1992 Annual Research Report
  • [Publications] Shirahata,S.(Shirahata,S.): "Estimate of variance of U-statistics" Communications in Statistics;Fheory & Metheds. 21. 2969-2981 (1992)

    • Related Report
      1992 Annual Research Report
  • [Publications] 白旗 慎吾(後藤 昌司): "統計的グラフィクスの最近の発展" 日本統計学会誌. 21. 331-351 (1992)

    • Related Report
      1992 Annual Research Report
  • [Publications] Isogai,T.(Hiratsuka,A.): "Study on sludge clewatering techniques using a statistical model…in view of both quantitry of filtrate and filtrate qualitry" 環境システム研究. 20. 231-241 (1992)

    • Related Report
      1992 Annual Research Report
  • [Publications] Chu,I.-S.(Chu,I.-S.): "Bootstrap selection of smoothing parameter for distribution function estimation" Mathematica Japonica. 38. (1993)

    • Related Report
      1992 Annual Research Report
  • [Publications] Chu,I.S,Shirahata,S.: "Law of the iterated logarithm for twoーsample empirical process and ChernoffーSavage statistics" Journal of Japan Statistical Society. 21. 85-95 (1991)

    • Related Report
      1991 Annual Research Report
  • [Publications] Shirahata,S.Chu,I.S.: "Confidence band for distribution function" Studies of Humanity and Social Sciences. 39. (1991)

    • Related Report
      1991 Annual Research Report
  • [Publications] Shirahata,S.Chu,I.S.: "Integrated squared errer of Kernelーtype estimation of distribution function" Annals of the Inststute of Statistical Mathematics. 45. (1992)

    • Related Report
      1991 Annual Research Report
  • [Publications] 磯貝 恭史,野口 博司: "特異値分解とその応用" 研究集録,人文・科学,社会科学編. 39. (1991)

    • Related Report
      1991 Annual Research Report
  • [Publications] Swe,M,Taniguchi: "Higherーorder asymptotic properties of a weighted estimation for Gaussian ARMA process" Time Series Analysis. 12. 83-93 (1991)

    • Related Report
      1991 Annual Research Report
  • [Publications] Hirano,K.Aki,S.Kuboki,H.Kashiwagi,N.: "On Ling's binomial and negative binomial distribution of order K" Statistics & Probability Letters. 11. 503-509 (1991)

    • Related Report
      1991 Annual Research Report

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Published: 1991-04-01   Modified: 2016-04-21  

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