A LOCAL CONSTANT ESTIMATOR FOR NONPARAMETRIC MIXED-EFFECTS MODELS WITH LONGITUDINAL DATA
纵向数据非参数混合效应模型的一个局部不变估计

Nonparametric kernel regression methods have been proposed for longitudinal data analysis recently (Lin and Carroll, 2000). A controversial question is whether the correlation among longitudinal data should be considered in the nonparametric kernel regression. Lin and Carroll (2000) have shown that the kernel estimator based on working-independence (ignoring the correlation) is most (asymptotically) efficient in a class of kernel GEE estimators. In this paper we propose a different class of kernel estimators based on the mixed-effects model approach that incorporates the correlation structure of longitudinal data naturally and efficiently. We show that our estimator achieves the same asymptotic efficiency as Lin and Carroll's estimator, but performs better in finite samples. The nonparametric curve estimates for both population and individual subjects (clusters) can be readily obtained from the proposed method. These good properties of the proposed estimator as well as easy implementation are attractive to practitioners.