You Jinhong, Zhou Haibo
Department of Biostatistics, University of North Carolina at Chapel Hill Chapel Hill, NC 27599-7400, USA.
Int J Stat Manag Syst. 2010 Jan 1;5(1-2):59-83.
This paper is concerned with the inference of seemingly unrelated (SU) varying-coefficient nonparametric regression models. We propose an estimation for the unknown coefficient functions, which is an extension of the two-stage procedure proposed by Linton, (2004) in the longitudinal data framework where they focused on purely nonparametric regression. We show the resulted estimators are asymptotically normal and more efficient than those based on only the individual regression equation even when the error covariance matrix is homogeneous. Another focus of this paper is to extend the generalized likelihood ratio technique developed by Fan, Zhang and Zhang (2001) for testing the goodness of fit of models to the setting of SU regression. A wild block bootstrap based method is used to compute -value of the test. Some simulation studies are given in support of the asymptotics. A real data set from an ongoing environmental epidemiologic study is used to illustrate the proposed procedures.
本文关注看似不相关的（SU）变系数非参数回归模型的推断。我们提出了一种对未知系数函数的估计方法，它是林顿（2004年）在纵向数据框架中提出的两阶段程序的扩展，在该框架中他们专注于纯非参数回归。我们表明，即使误差协方差矩阵是齐次的，所得估计量也是渐近正态的，并且比仅基于单个回归方程的估计量更有效。本文的另一个重点是将范、张和张（2001年）开发的用于检验模型拟合优度的广义似然比技术扩展到SU回归的设定中。基于野生块自助法的方法用于计算检验的p值。给出了一些模拟研究以支持渐近性。使用来自正在进行的环境流行病学研究的一个真实数据集来说明所提出的程序。
