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正态总体均值与标准差比在序约束下的广义p-值检验 被引量：2

Testing Ratios of Means to Standard Deviations from Normal Populations under Order Restrictions with Generalized p Values
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摘要 本文利用广义p-值和U-I检验法研究了多个正态总体均值与标准差比在简单半序和树序约束下的检验问题.提出了广义检验变量,得到了多个正态总体均值与标准差比在简单半序和树序约束下检验问题的广义p-值.同时运用MonteCarlo方法给出了模拟结果. A procedure for testing ratios of means to standard deviations from normal populations under semiorder restriction and tree order restriction is developed. The testing is performed on the basis of the generalized p value approach and U-I test and involves a one-dimensional numerical integration. The problem is always encountered in biology, medication, business investment, telecommunication, and so on. We propose the generalized test variable and obtain the generalized p values of the testing problem. Finally, simulation results are given.
作者 李树有 史宁中 张宝学
机构地区 辽宁工业大学数理系 东北师范大学数学与统计学院
出处 《应用概率统计》 CSCD 北大核心 2009年第1期77-85,共9页 Chinese Journal of Applied Probability and Statistics
基金 国家自然科学基金(10431010 10571020) 辽宁省教育厅基金(20060409)资助.
关键词 广义P-值 广义检验变量 U—I检验法 正态总体 半序约束. Generalized p value, generalized test variable, U-I test normal population, semi-order restriction.
分类号 O212.1 [理学—概率论与数理统计]
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参考文献5

  • 1Tsui, K.W. and Weerahandi, S., Generalized p values in significance testing of hypotheses in the presence of nuisance parameters, Journal of the American Statistical Association, 84(1989), 602-607.
  • 2Weerahandi, S., Testing variance components in mixed models with generalized p values, Journal of the American Statistical Association, 86(1991), 151-153.
  • 3Chou, Y.M. and Owen, D.B., A likelihood ratio test for the equality of proportions of two normal populations, Commun. Statist. Theory Meth., 8(1991), 2357-2374.
  • 4Shi, N.Z., Maximum likelihood estimation of means and variances from normal populations and simultaneous order restriction, J. Multivariate Anal., 50(1994), 282-293.
  • 5Shi, N.Z. and Jiang, H., Maximum likelihood estimation of isotonic normal means with unknown variances, J. Multivariate Anal., 64(1998), 183-195.

同被引文献9

  • 1Robertson T,Wright F T,Dykstra R L. Order Restricted Statistical Inference[M].New Jersey:John Wiley & Sons Inc,1988.
  • 2Silvapulle M J,Sen P K. Constrained Statistical Inference:Inequality,Order and Shape Restrictions[M].New Jersey:John Wiley & Sons Inc,2005.
  • 3Hayter A J. A One-Sided Studentized Range Test for Testing against a Simple Order Alternative[J].Journal of the American Statistical Association,1990,(411):778-785.
  • 4LIU Lin. Simultaneous Statistical Inference for Monotone Dose-Response Means[D].Newfoundlan:Memorial Universtiy of Newfoundland,2001.
  • 5LIU Lin,Lee C C,PENG Jian-an. Max-Min Multiple Comparison Procedure for Isotonic Dose-Response Curves[J].Journal of Statistical Planning and Inference,2002,(1/2):133-141.
  • 6史宁中.统计检验的理论与方法[M]北京:科学出版社,2008.
  • 7SHANG Jun-feng,Cavanaugh J E,Wright F T. A Bayesian Multiple Comparison Procedure for Order-Restricted Mixed Models[J].International Statistical Review,2008,(02):268-284.
  • 8Oh M S,Shin D W. A Unified Bayesian Inference on Treatment Means with Order Constraints[J].Computational Statistics and Data Analysis,2011,(01):924-934.
  • 9Chou Y M,Owen D B. A Likelihood Ratio Test for the Equality of Proportions of Two Normal Populations[J].Communications in Statistics-Theory and Methods,1991,(08):2357-2374.

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应用概率统计
2009年 第1期

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