Analysis of longitudinal data with semiparametric estimation of covariance function
Analysis of longitudinal data with semiparametric estimation of covariance function
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DOI：
10.1198/016214507000000095
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发表时间：
2007-06-01
影响因子：
3.7
通讯作者：
Li, Runze
中科院分区：
文献类型：
--
作者：
Fan, Jianqing;Huang, Tao;Li, Runze
提高回归系数的效率和预测个体的轨迹是纵向数据分析中的两个重要方面。两者都涉及协方差函数的估计。然而，在估计在不规则时间点收集的纵向数据的协方差函数方面出现了挑战。提出了一类关于协方差函数的半参数模型，该模型在引入参数相关结构的同时允许非参数方差函数。给出了估计非参数方差函数的核估计。提出了两种估计相关结构参数的方法--拟似然方法和最小广义方差法。介绍了纵向数据的半参数变系数部分线性模型，提出了一种基于剖面加权最小二乘法的模型系数估计方法。研究了所提出的估计方法的抽样性质，建立了所得估计量的渐近正态分布。通过蒙特卡罗模拟研究对所提方法的有限样本性能进行了评估。通过对一个实际数据实例的分析，说明了所提出的方法。
Improving efficiency for regression coefficients and predicting trajectories of individuals are two important aspects in the analysis of longitudinal data. Both involve estimation of the covariance function. Yet challenges arise in estimating the covariance function of longitudinal data collected at irregular time points. A class of semiparametric models for the covariance function by that imposes a parametric correlation structure while allowing a nonparametric variance function is proposed. A kernel estimator for estimating the nonparametric variance function is developed. Two methods for estimating parameters in the correlation structure - a quasi-likelihood approach and a minimum generalized variance method-are proposed. A semiparametric varying coefficient partially linear model for longitudinal data is introduced, and an estimation procedure for model coefficients using a profile weighted least squares approach is proposed. Sampling properties of the proposed estimation procedures are studied, and asymptotic normality of the resulting estimators is established. Finite-sample performance of the proposed procedures is assessed by Monte Carlo simulation studies. The proposed methodology is illustrated with an analysis of a real data example.