Li Runze, Li Yan
Department of Statistics and The Methodology Center, Pennsylvania State University, University Park, PA 16802-2111, USA,
Acta Math Appl Sin. 2009 Jul 1;25(3):427-444. doi: 10.1007/s10255-008-8813-3.
In many statistical applications, data are collected over time, and they are likely correlated. In this paper, we investigate how to incorporate the correlation information into the local linear regression. Under the assumption that the error process is an auto-regressive process, a new estimation procedure is proposed for the nonparametric regression by using local linear regression method and the profile least squares techniques. We further propose the SCAD penalized profile least squares method to determine the order of auto-regressive process. Extensive Monte Carlo simulation studies are conducted to examine the finite sample performance of the proposed procedure, and to compare the performance of the proposed procedures with the existing one. From our empirical studies, the newly proposed procedures can dramatically improve the accuracy of naive local linear regression with working-independent error structure. We illustrate the proposed methodology by an analysis of real data set.
在许多统计应用中，数据是随时间收集的，并且它们可能是相关的。在本文中，我们研究如何将相关信息纳入局部线性回归。在误差过程是自回归过程的假设下，提出了一种使用局部线性回归方法和轮廓最小二乘法的非参数回归新估计程序。我们进一步提出了SCAD惩罚轮廓最小二乘法来确定自回归过程的阶数。进行了广泛的蒙特卡罗模拟研究，以检验所提出程序的有限样本性能，并将所提出程序的性能与现有程序进行比较。从我们的实证研究来看，新提出的程序可以显著提高具有工作独立误差结构的朴素局部线性回归的准确性。我们通过对真实数据集的分析来说明所提出的方法。
