半参数广义线性混合效应模型的估计及其渐近性质  

Asymptotic Properties of Estimation in Generalized Partial Linear Mixed Models

作　　者：张浩[1] 朱仲义[2] 

机构地区：[1]华东师范大学统计系,上海200062 [2]复旦大学统计系,上海200433

出　　处：《应用概率统计》2009年第2期171-184,共14页Chinese Journal of Applied Probability and Statistics

基　　金：国家自然科学基金项目(10671038);上海市重点学科建设项目(B210)资助

摘　　要：半参数广义线性混合效应模型在心理学、生物育种、医学等领域有广泛的应用.Zhang(1998)用最大惩罚似然函数的方法(MPLE)对模型的参数和非参数部分进行了估计,然而Zhang(1998)MPLE方法只适用于正态数据模型.对于泊松等常用的模型,通常的方法是将随机效应看作缺失数据,再引入EM算法.本文基于McCulloch(1997)提出的MCNR算法,将此算法推广到半参数广义线性混合效应模型中并得到相应的估计算法.对于非参数部分,本文采用P样条拟合并利用GCV方法选取光滑参数,同时证明了所得估计的相合性和渐近正态性.最后,通过模拟和实例与其它算法作比较验证本文估计方法的有效性.Semiparametric models are useful in psychological, biological and medical application. Zhang （1998） used maximum penalized likelihood estimation （MPLE） to estimate both of the parametric and nonparao metric parameters. Unfortunately, MPLE proposed by Zhang （1998） can only be applied to the Gaussian Models. In general, in order to estimate the parametric and nonparametric part in generalized partial linear mixed models, we choose to treat the random effects as the missing data and construct a Monte Carlo version of the EM algorithm. Based on the MCNR algorithm proposed by McCulloch （1997）, we, in this paper, extend the algorithm to the generalized partial linear mixed models （GPLMM） so that it may estimate both of the parameters and nonpaxameters simultaneously. In the new algorithm, we approximate the nonparametric function in CPLMM by P-spline and use GCV to choose the smoothing parameter. Meanwhile, we also give the proofs and the asymptotic properties of the estimators. Finally, in order to test the reliability of the method, the proposed algorithm is illustrated in the simulation analysis and one real data set.

关 键 词：半参数模型 MCNR算法 混合效应 广义线性模型 渐近性质 

分 类 号：O212.1[理学—概率论与数理统计]