Local Linear Regression for Data with AR Errors  

作　　者：Runze Li Yan Li 

机构地区：[1]Department of Statistics and The Methodology Center, Pennsylvania State University, University Park, PA 16802-2111, USA [2]Cards Acquisitions, Capital One Financial Inc 1680 Capital One Dr, 19050-0701, McLean, VA 22102, USA

出　　处：《Acta Mathematicae Applicatae Sinica》2009年第3期427-444,共18页应用数学学报（英文版）

基　　金：supported by National Institute on Drug Abuse grant R21 DA024260;Yan Li issupported by National Science Foundation grant DMS 0348869 as a graduate research assistant

摘　　要：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.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.

关 键 词：Auto-regressive error local linear regression partially linear model profile least squares SCAD 

分 类 号：TP317[自动化与计算机技术—计算机软件与理论] TQ221.211[自动化与计算机技术—计算机科学与技术]