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含估计参数的加权经验过程 被引量：1

THE WEIGHTED EMPIRICAL PROCESSES WITH ESTIMATED PARAMETERS
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摘要 在讨论(广义)非参数似然比拟合优度检验时,加权经验过程理论是一个非常重要的基础.但对含估计参数的加权经验过程理论,目前文献中很少讨论.对含估计参数的加权经验过程的上界型和积分型两种统计量的近似分布进行了讨论,给出了较一般的结果.所得结论可以为进一步讨论复合零假设下(广义)非参似然比拟合优度检验提供理论基础. The theory of weighted empirical processes is an important element for （generalized） nonparametric likelihood ratio goodness of fit test. There are few papers to discuss the weighted empirical processes with estimated parameters. This paper is concerned with the approximation distribution of the weighted empirical processes systematically. The results will provide a certain theoretical basis for （generalized） nonparametric likelihood ratio goodness of fit test with estimated parameters.
作者 张军舰
机构地区 北京工业大学应用数理学院 广西师范大学数学科学学院
出处 《系统科学与数学》 CSCD 北大核心 2009年第5期608-616,共9页 Journal of Systems Science and Mathematical Sciences
基金 广西自然科学基金(桂科自0832102) 广西师范大学博士科研启动基金 国家自然科学基金(10661003)资助课题
关键词 加权经验过程 估计参数 拟合优度检验 The weighted empirical processes, estimated parameter, goodness of fit.
分类号 O212.1 [理学—概率论与数理统计]
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参考文献10

  • 1Berk R H,Jones D H.Relatively optimal combinations of test statistics.Scand.J.Statist.,1978,5:158-162.
  • 2Jager L,Wellner J A.A new goodness of fit test:The reversed Berk-Jones statistic.Technical report,Department of Statistics,University of Washington.http://www.stat.washington.edu/www/research/reports/2004/tr443.ps,2004.
  • 3Zhang J J.Generalized nonparametric likelihood ratio for goodness-of-fit tests.Ph.D Dissertation,Chinese Academy of Sciences,2006.
  • 4Csorgo M,Horvath L.Weighted Approximations in Prability and Statistics.John Wiley and Sons,England,1993.
  • 5Darling D A.The Cramer-Smirnov test in the parametric case.Ann.Math.Statist.,1955,26:1-20.
  • 6Del Barrio E.Empirical and quantile processes in the asymptotic theory of goodness-of-fit test.http://www.eio.uva.es/ems/Goodness_of_fit-Laredo_2004.pdf,2004.
  • 7Genz M,Haeusler E.Empirical processes with estimated parameters under auxiliary information.J.Com.App.Math.,2006,186:191-216.
  • 8Shorack G R,Wellner J A.Empirical Processes with Applications to Statistics.New York:Wiley,1986.
  • 9Jaeschke D.The asymptotic distribution of the supremum of the standardized empirical distribution function on subintervals.Ann.Statist.,1979,7(1):108-115.
  • 10Babu G J,Rao C R.Goodness-of-fit tests when parameters are estimated.Sankhya.,2004,66:63-74.

同被引文献7

  • 1Robert H. Berk,Douglas H. Jones.Goodness-of-fit test statistics that dominate the Kolmogorov statistics[J]. Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete . 1979 (1)
  • 2Shorack G R,Wellner J A.Empirical Processes with Applications to Statistics. . 1986
  • 3Jager L,,Wellner J A.A new goodness-of-fit test:thereversed Berk-Jones statistic. http:∥www.stat.washington.edu/www/research/reports/2004/tr443.pdf . 2005
  • 4Wellner J A,Koltchinskii V.A note on the asymptotic distribution of Berk-Jones type statistics under the null hypothesis:High dimensional probability. . 2003
  • 5Jaeschke D.The asymptotic distribution of the supremum of the standardized empirical distribution function on subintervals. The Annals of Statistics . 1979
  • 6Babu,GJ,Rao,CR.Goodness-of-fit tests when parameters are estimated. Sankhyā: Indian J Statist . 2004
  • 7Einmahl,J.H.J.,McKeague,I.W.Empirical likelihood based hypothesis testing. Bernoulli . 2003

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系统科学与数学
2009年 第5期

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