TY - JOUR
T1 - Local linear regression for data with AR errors
AU - Li, Runze
AU - Li, Yan
N1 - Funding Information:
Manuscript received January 26, 2009. 1Runze Li’s research was supported by National Institute on Drug Abuse grant R21 DA024260, supported by National Science Foundation grant DMS 0348869 as a graduate research assistant.
PY - 2009/7
Y1 - 2009/7
N2 - 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.
AB - 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.
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U2 - 10.1007/s10255-008-8813-3
DO - 10.1007/s10255-008-8813-3
M3 - Article
C2 - 20161374
AN - SCOPUS:66749097331
SN - 0168-9673
VL - 25
SP - 427
EP - 444
JO - Acta Mathematicae Applicatae Sinica
JF - Acta Mathematicae Applicatae Sinica
IS - 3
ER -