Nonparametric smoothing estimates of time-varying coefficient models with longitudinal data
Nonparametric smoothing estimates of time-varying coefficient models with longitudinal data
复制标题
DOI：
10.1093/biomet/85.4.809
复制
发表时间：
1998-12-01
期刊：
影响因子：
2.7
通讯作者：
Yang, LP
中科院分区：
文献类型：
--
作者：
Hoover, DR;Rice, JA;Yang, LP
本文考虑了具有重复测量的变系数模型（Y-ij，X-ij，t（ij））的非参数估计，其中i=1，…，n和j=1，…，ni，其中x（ij）=（X-ij 0，...，X-ijk）（T）和（Y-ij，X-ij，t（ij））分别表示第i例受试者的第j个结局、协变量和时间设计点。这里考虑的模型是Y-ij =X（ij）（T）beta（t（ij））+ β（i）（t（ij）），其中beta（t）=（beta（0）（t），.，beta（k）（t））（T），对于k大于或等于0，是感兴趣的光滑非参数函数，并且β（i）（t）是零均值随机过程。假设测量对于不同受试者是独立的，但可以在每个受试者内的不同时间点相关。对于这种重复测量的数据，我们导出了beta（t）的两种非参数估计，即光滑样条估计和局部加权多项式估计。提出了一个交叉验证准则，用于选择相应的平滑参数。渐近性质，如一致性，收敛速度和渐近均方误差，建立核估计，局部多项式的特殊情况。这些渐近结果提供了有用的见解，我们的一般估计方法的可靠性。一个基于性别、HIV感染状况和母亲维生素A水平预测HIV感染母亲所生儿童生长的例子表明，该模型和相应的非参数估计在流行病学研究中是有用的。
This paper considers nonparametric estimation in a varying coefficient model with repeated measurements (Y-ij,X-ij,t(ij)), for i=1,...,n and j=1,...,ni, where x(ij)=(X-ij0,..., X-ijk)(T) and (Y-ij,X-ij, t(ij)) denote the jth outcome, covariate and time design points, respectively, of the ith subject. The model considered here is Y-ij =X(ij)(T)beta(t(ij))+ epsilon(i)(t(ij)), where beta(t) = (beta(0)(t),..., beta(k)(t))(T), for k greater than or equal to 0, are smooth nonparametric functions of interest and epsilon(i)(t) is a zero-mean stochastic process. The measurements are assumed to be independent for different subjects but can be correlated at different time points within each subject. Two nonparametric estimators of beta(t), namely a smoothing spline and a locally weighted polynomial, are derived for such repeatedly measured data. A crossvalidation criterion is proposed for the selection of the corresponding smoothing parameters. Asymptotic properties, such as consistency, rates of convergence and asymptotic mean squared errors, are established for kernel estimators, a special case of the local polynomials. These asymptotic results give useful insights into the reliability of our general estimation methods. An example of predicting the growth of children born to HIV infected mothers based on gender, HIV status and maternal vitamin A levels shows that this model and the corresponding nonparametric estimators are useful in epidemiological studies.