Wavelet estimation of a regression function with a sharp change point in a random design

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In a random design nonparametric regression model, this paper deals with the detection of a sharp change point and the estimation of a regression function with a single jump point. A method based on design transformation and binning is used in order to convert a random design into an equispaced design whose number of points is a power of 2. Using the continuous wavelet transform of the data, we construct a sharp change point estimator and obtain its rate of convergence. Wavelet methods are well known for their good adaptivity around Sudden local changes; however, in practice, the Gibbs phenomenon still exists. This difficulty is overcome by suitably adjusting the data with preliminary estimators for the location and the size of discontinuity. Global and local asymptotic results of the proposed method are obtained. The method is also tested on simulated examples and the results show that the proposed method alleviates the Gibbs phenomenon. (c) 2005 Elsevier B.V. All rights reserved.
Publisher
ELSEVIER SCIENCE BV
Issue Date
2006-07
Language
English
Article Type
Article
Citation

JOURNAL OF STATISTICAL PLANNING AND INFERENCE, v.136, no.7, pp.2381 - 2394

ISSN
0378-3758
DOI
10.1016/j.jspi.2005.08.017
URI
http://hdl.handle.net/10203/285766
Appears in Collection
MA-Journal Papers(저널논문)
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