纵向数据下部分线性模型基于经验似然的变量选择
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摘要
针对纵向数据下的部分线性模型,建立基于经验似然方法的变量选择的信息准则,证明新变量选择方法的渐近性质,并模拟研究比较参数信息准则与基于经验似然的信息准则的有限样本性质.结果表明,基于经验似然方法的信息准则克服了参数似然函数有时较难得到的困难,模型选择效果较好.
For the partially linear model with longitudinal data,we established the information criteria of variable selection based on empirical likelihood method,and proved the asymptotic properties of the new variable selection method.We simulated and compared the limited sample properties of parameter and information criteria based on empirical likelihood.The results show that the information criteria based on empirical likelihood method overcomes the difficulty that the parameter likelihood functions are sometimes difficult to obtain,and the model selection effect is better.
For the partially linear model with longitudinal data,we established the information criteria of variable selection based on empirical likelihood method,and proved the asymptotic properties of the new variable selection method.We simulated and compared the limited sample properties of parameter and information criteria based on empirical likelihood.The results show that the information criteria based on empirical likelihood method overcomes the difficulty that the parameter likelihood functions are sometimes difficult to obtain,and the model selection effect is better.
引文
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[11]CUI Hengjian,CHEN Songxi.Empirical Likelihood Confidence Region for Parameter in the Errors-in-Variable Models[J].J Multivariate Anal,2003,84(1):101-115.
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[13]Variyath A M,CHEN Jiahua,Abraham B.Empirical Likelihood Based Variable Selection[J].J Stat Plann Infer,2010,140(4):971-981.
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[2]HU Zonghui,WANG Naisyin,Carroll R J.Profile-Kernel versus Backfitting in the Partially Linear Models for Longitudinal/Clustered Data[J].Biometrika,2004,91(2):251-262.
[3]薜留根,朱力行.纵向数据下部分线性模型的经验似然推断[J].中国科学(A辑:数学),2007,37(1):31-44.(XUE Liugen,ZHU Lixing.Empirical Likelihood Semiparametric Regression Analysis for Longitudinal Data[J].Science in China(Series A:Mathematics),2007,37(1):31-44.)
[4]ZHANG Tao,ZHU Zhongyi.Efficient Inference Based on Block Empirical Likelihood for Longitudinal Partially Linear Regression Models[J].Chinese Journal of Applied Probability and Statistics,2010,26(3):323-335.
[5]柳长青,赵培信.纵向部分线性模型的分块经验似然比检验[J].数学的实践与认识,2015,45(19):135-141.(LIU Changqing,ZHAO Peixin.Block Empirical Likelihood Ratio Test for Longitudinal Partially Linear Models[J].Mathematics in Practice and Theory,2015,45(19):135-141.)
[6]Owen A B.Empirical Likelihood Ratio Confidence Intervals for a Single Functional[J].Biometrika,1988,75(2):237-249.
[7]Owen A B.Empirical Likelihood Ratio Confidence Regions[J].Ann Statist,1990,18(1):90-120.
[8]Owen A B.Empirical Likelihood for Linear Models[J].Ann Statist,1991,19(4):1725-1747.
[9]QIN Jing,Lawless J.Empirical Likelihood and General Estimating Equations[J].Ann Statist,1994,22(1):300-325.
[10]WANG Qihua,LI Gang.Empirical Likelihood Semiparametric Regression Analysis under Random Censorship[J].J Multivariate Anal,2002,83(2):469-486.
[11]CUI Hengjian,CHEN Songxi.Empirical Likelihood Confidence Region for Parameter in the Errors-in-Variable Models[J].J Multivariate Anal,2003,84(1):101-115.
[12]XUE Liugen,ZHU Lixing.Empirical Likelihood for Single-Index Models[J].J Multivariate Anal,2006,97(6):1295-1312.
[13]Variyath A M,CHEN Jiahua,Abraham B.Empirical Likelihood Based Variable Selection[J].J Stat Plann Infer,2010,140(4):971-981.
[14]CHEN Jiahua,Variyath A M,Abraham B.Adjusted Empirical Likelihood and Its Properties[J].J Comput Graph Statist,2008,17(2):426-443.
[15]Thall P F,Vail S C.Some Covariance Models for Longitudiual Count Data with Overdispersion[J].Biometrics,1990,46(3):657-671.