KERNEL SMOOTHING ON VARYING COEFFICIENT MODELS WITH LONGITUDINAL DEPENDENT VARIABLE
KERNEL SMOOTHING ON VARYING COEFFICIENT MODELS WITH LONGITUDINAL DEPENDENT VARIABLE
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发表时间：
2000
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通讯作者：
Colin O. Wu;Chin‐Tsang Chiang
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作者：
Colin O. Wu;Chin‐Tsang Chiang
本文考虑了一个具有纵向因变量和横截面协变量的非参数变系数回归模型。假设因变量和协变量之间的关系在特定时间点是线性的，但允许系数随时间变化。提出了两种基于分量局部最小二乘准则的核估计器来估计时变系数。交叉验证准则和引导程序分别用于选择数据驱动的带宽和构造置信区间。我们的估计的理论性质，通过他们的渐近均方误差和平均积分平方误差。我们的程序的有限样本性质进行了研究，通过模拟研究。我们的程序的应用说明通过一个流行病学的例子，预测吸烟的影响，艾滋病毒感染前的CD4细胞的百分比和年龄在艾滋病毒感染的CD4细胞的百分比之间的消耗艾滋病毒感染者。
This paper considers a nonparametric varying coefficient regression model with longitudinal dependent variable and cross-sectional covariates. The relation- ship between the dependent variable and the covariates is assumed to be linear at a specific time point, but the coefficients are allowed to change over time. Two kernel estimators based on componentwise local least squares criteria are proposed to esti- mate the time varying coefficients. A cross-validation criterion and a bootstrap pro- cedure are used for selecting data-driven bandwidths and constructing confidence intervals, respectively. The theoretical properties of our estimators are developed through their asymptotic mean squared errors and mean integrated squared errors. The finite sample properties of our procedures are investigated through a simulation study. Applications of our procedures are illustrated through an epidemiological example of predicting the effects of cigarette smoking, pre-HIV infection CD4 cell percentage and age at HIV infection on the depletion of CD4 cell percentage among HIV infected persons.