Change point estimation by local linear smoothing

JOURNAL OF MULTIVARIATE ANALYSIS

卷:83

Article

Grégoire, G ; Hamrouni, Z

关键词: nonparametric regression;    local linear regression;    change points;    compound Poisson processes;   

DOI  :  10.1006/jmva.2001.2038

来源: Elsevier

【 摘 要 】

We consider the problem of estimating jump points in smooth curves. Observations (X-i, Y-i) i = 1,..., n from a random design regression function are given. We focus essentially on the basic situation where a unique change point is present in the regression function. Based on local linear regression, a jump estimate process t --> (gamma) over cap (t) is constructed. Our main result is the convergence to a compound Poisson process with drift, of a local dilated-rescaled version of (gamma) over cap (t), under a positivity condition regarding the asymmetric kernel involved. This result enables us to prove that our estimate of the jump location converges with exact rate n(-1) without any particular assumption regarding the bandwidth h(n). Other consequences such as asymptotic normality are investigated and some proposals are provided for an extension of this work to more general situations. Finally we present Monte-Carlo simulations which give evidence for good numerical performance of our procedure. (C) 2001 Elsevier Science (USA).

【 授权许可】

Free