Change point estimators by local polynomial fits under a dependence assumption

TY - JOUR

T1 - Change point estimators by local polynomial fits under a dependence assumption

AU - Lin, Zhengyan

AU - Li, Degui

AU - Chen, Jia

N1 - (C) 2008 Elsevier Inc. All rights reserved.

PY - 2008/11

Y1 - 2008/11

N2 - We study a random design regression model generated by dependent observations, when the regression function itself (or its nu-th derivative) may have a change or discontinuity point. A method based on the local polynomial fits with one-sided kernels to estimate the location and the jump size of the change point is applied in this paper. When the jump location is known, a central limit theorem for the estimator of the jump size is established; when the jump location is unknown, we first obtain a functional limit theorem for a local dilated-rescaled version estimator of the jump size and then give the asymptotic distributions for the estimators of the location and the jump size of the change point. The asymptotic results obtained in this paper can be viewed as extensions of corresponding results for independent observations. Furthermore, a simulated example is given to show that our theory and method per-form well in practice. 

AB - We study a random design regression model generated by dependent observations, when the regression function itself (or its nu-th derivative) may have a change or discontinuity point. A method based on the local polynomial fits with one-sided kernels to estimate the location and the jump size of the change point is applied in this paper. When the jump location is known, a central limit theorem for the estimator of the jump size is established; when the jump location is unknown, we first obtain a functional limit theorem for a local dilated-rescaled version estimator of the jump size and then give the asymptotic distributions for the estimators of the location and the jump size of the change point. The asymptotic results obtained in this paper can be viewed as extensions of corresponding results for independent observations. Furthermore, a simulated example is given to show that our theory and method per-form well in practice. 

KW - Functional limit theorem

KW - Random design model

KW - NONPARAMETRIC REGRESSION

KW - TIME-SERIES

KW - Local polynomial fits

KW - Change point

KW - alpha-mixing

UR - http://www.scopus.com/inward/record.url?scp=54049103239&partnerID=8YFLogxK

U2 - 10.1016/j.jmva.2008.02.036

DO - 10.1016/j.jmva.2008.02.036

M3 - Article

SN - 0047-259X

VL - 99

SP - 2339

EP - 2355

JO - Journal of Multivariate Analysis

JF - Journal of Multivariate Analysis

IS - 10

ER -