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Change point estimators by local polynomial fits under a dependence assumption

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Publication details

JournalJournal of Multivariate Analysis
DatePublished - Nov 2008
Issue number10
Volume99
Number of pages17
Pages (from-to)2339-2355
Original languageEnglish

Abstract

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. 

Bibliographical note

(C) 2008 Elsevier Inc. All rights reserved.

    Research areas

  • Functional limit theorem, Random design model, NONPARAMETRIC REGRESSION, TIME-SERIES, Local polynomial fits, Change point, alpha-mixing

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