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Behrens-Fisher问题的正态逼近 被引量：2

Normal Approximation to the Behrens-Fisher Problem
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摘要 本文提出用基于得分检验的正态逼近方法来解决Behrens-Fisher问题,即比较方差比未知时两正态总体的均值。模拟结果显示:在所有的研究情况下,这种方法都能很好地控制第一类错误,检验功效也不差;而最常用的Welch近似t检验在样本量不等时大多数情况都不能控制第一类错误。 Normal approximation based on the score test is proposed to solve the Behrens-Fisher problem, that is to compare the means of two normal populations with the ratio of the population variances unknown. Simulation results suggest that our new approach can definitely control the type I error rates with reasonable powers under all studied conditions while the popular Weleh＇s approximate t-test cannot for most cases when the sizes of two samples are unequal.
作者 金华 郑圣听 陈伟权
机构地区 华南师范大学数学科学学院 华南师范大学概率统计系 国际知名杂志
出处 《统计研究》 CSSCI 北大核心 2009年第11期106-108,共3页 Statistical Research
基金 全国统计科学研究计划重点项目“诊断技术等效性检验的统计方法及其应用研究”(2006B45)资助
关键词 Behrens-Fisher问题 Welch近似t检验 得分检验 正态逼近 Behrens-Fisher problem Welch＇s approximate t-test Score test Normal approximation
分类号 O212 [理学—概率论与数理统计]
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参考文献14

  • 1BV Behrens. Ein Beitrag zur Fehlerberechnung bei wenige Beobachtungen[J]. Landwirtch. Jb. 1929(6) :807 - 837.
  • 2RA Fisher. The fidueial argument in statistical inference [ J ]. The Annals of Eugenics, 1935(6) :141 - 172.
  • 3PL Hsu. Statistical Research Memoirs. Department of Statistics, University College London, 1938.
  • 4BL Welch. The specification of rules for rejecting too variable a product, with particular reference to an electric lamp problem[J]. J. R, Statist. Sec. Suppl. ,1936(3):29-48.
  • 5BL Welch. The significance of the difference between means when the population variances are unequal[J]. Biometrika, 1938(3/4): 350 - 362.
  • 6YY Wang. Probabilities of the type I errors of Welch tests for the Behrens-Fisher problem[J]. J. Am. Statist. Assoc, 1971(3): 605- 608.
  • 7BL Welch. The generalization of Student's problem when several populations are involved[J]. Biometrika, 1947(1/2) : 28 - 35.
  • 8BL Welch. Appendix to Mrs. Aspin's tables. Biometrika, 1949(3/4): 293 - 296.
  • 9AA Aspin. An examination and further development of a formula arising in the problem of comparing two mean values[J]. Biometrika, 1948( 1/ 2): 88-96.
  • 10AA Aspin. Tables for use in comparisons whose accuracy involves two variances, separately estimated (with appendix by B. L. Welch)[J]. Biometfika, 1949(3/4) : 290 - 296.

同被引文献23

  • 1Behrens B V . Ein Beitrag zur Fehlerberechnung Bei Wenige Beobachtungen[J].Landwirtch.Jb., 1929,6.
  • 2Fisher R A. The Fiducial Argument in Statistical Inference[J].Annals of Eugenics, 1935,(6).
  • 3Welch B L. The Specification of Rules for Rejecting Too Variable a Product, with Particular Reference to an Electric Lamp Problem[J]. Supplement to the Journal of the Royal Statistical Society,1936,3.
  • 4Welch B L . The Significance of the Difference Between Two Means when the Population Variances are Unequal[J]. Biometrika, 1938,29.
  • 5Tsui K W , Weerahandi S . Generalized P-Values in Significance Testing of Hypotheses in the Presence of Nuisance Parameters[J]. Journal of the American Statistical Association, 1989,84.
  • 6Krishnamoorthy K , Lu F ,Mathew T . A Parametric Bootstrap Ap- proach for ANOVA with Unequal Variances: Fixed and Random Mod- els [J]. Computational Statistics & Data Analysis, 2007,51.
  • 7Efron B, Tibshirani R J. An Introduction to Bootstrap[M]. Chapman & Hall London, 1993.
  • 8Xu L W , Yang F Q , Abula A , et al . A Parametric Bootstrap Ap- proach for Two-way ANOVA in Presence of Possible Interactions with Unequal Variances [J]. Journal of Multivariate Analysis, 2013, 115.
  • 9Tian L L, Ma C X ,Vexler A. A Parametric Bootstrap Test for Com- paring Heteroscedastic Regression Models [J]. Comm. Statist. Simu- lation Comput,2009,38.
  • 10Behrens B V. Ein beitrag zur fehlerberechnung bei wenige beobachtungen [J]. Landwirtch. Jb., 1929, (6): 807-837.

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统计研究
2009年 第11期

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