Change point estimators by local polynomial fits under a dependence assumption

Zhengyan Lin, Degui Li*, Jia Chen

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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. 

Original languageEnglish
Pages (from-to)2339-2355
Number of pages17
JournalJournal of Multivariate Analysis
Issue number10
Publication statusPublished - Nov 2008

Bibliographical note

(C) 2008 Elsevier Inc. All rights reserved.


  • Functional limit theorem
  • Random design model
  • Local polynomial fits
  • Change point
  • alpha-mixing

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