Chen Zhao, Li Runze, Li Yan
Princeton University, Pennsylvania State University, eBay Inc.
Stat Sin. 2015 Apr;25(2):709-724. doi: 10.5705/ss.2012.301.
Varying coefficient model has been popular in the literature. In this paper, we propose a profile least squares estimation procedure to its regression coefficients when its random error is an auto-regressive (AR) process. We further study the asymptotic properties of the proposed procedure, and establish the asymptotic normality for the resulting estimate. We show that the resulting estimate for the regression coefficients has the same asymptotic bias and variance as the local linear estimate for varying coefficient models with independent and identically distributed observations. We apply the SCAD variable selection procedure (Fan and Li, 2001) to reduce model complexity of the AR error process. Numerical comparison and finite sample performance of the resulting estimate are examined by Monte Carlo studies. Our simulation results demonstrate the proposed procedure is much more efficient than the one ignoring the error correlation. The proposed methodology is illustrated by a real data example.
变系数模型在文献中一直很流行。在本文中，当随机误差是自回归（AR）过程时，我们提出了一种针对其回归系数的轮廓最小二乘估计方法。我们进一步研究了所提出方法的渐近性质，并建立了所得估计量的渐近正态性。我们表明，所得的回归系数估计量与具有独立同分布观测值的变系数模型的局部线性估计量具有相同的渐近偏差和方差。我们应用SCAD变量选择方法（Fan和Li，2001）来降低AR误差过程的模型复杂性。通过蒙特卡罗研究检验了所得估计量的数值比较和有限样本性能。我们的模拟结果表明，所提出的方法比忽略误差相关性的方法效率更高。通过一个实际数据例子说明了所提出的方法。
