半参数广义线性混合效应模型的估计及其渐近性质

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, 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, 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, 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. 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, 时证明了所得估计的相合性和渐近正态性. 最后, 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.

Asymptotic Properties of Estimation in GeneralizedPartial Linear Mixed Models

Semiparametric models are useful in sychological, biological and medical application. Zhang (1998) usedmaximum penalized likelihood estimation (MPLE) to estimate both ofthe parametric and nonparametric parameters. Unfortunately, MPLEproposed by Zhang (1998) can only be applied to the Gaussian Models.In general, in order to estimate the parametric and nonparametricpart in generalized partial linear mixed models, we choose to treatthe random effects as the missing data and construct a Monte Carloversion of the EM algorithm. Based on the MCNR algorithm proposed byMcCulloch (1997), we, in this paper, extend the algorithm to the eneralized partial linear mixed models (GPLMM) so that it mayestimate both of the parameters and nonparameters simultaneously. Inthe new algorithm, we approximate the nonparametric function inGPLMM by P-spline and use GCV to choose the smoothing parameter.Meanwhile, we also give the proofs and the asymptotic properties ofthe estimators. Finally, in order to test the reliability of themethod, the proposed algorithm is illustrated in the simulationanalysis and one real data set.