Estimation of a regression function with a sharp change point using boundary wavelets

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We propose a sharp change point estimator based on the differences between right and left boundary wavelet smoothers. It is constructed by applying a two-step procedure to the observed data and has the minimax convergence rate. Next, we estimate the regression function with boundary wavelets in the left and right regions of the estimated jump point separately. This method helps us to capture the feature of a discontinuity in practice. Both mean integrated squared error and mean squared error of the estimated function are derived and we then show that these rates of convergence are the same as the case in which a jump point does not exist. Simulated examples demonstrate the improved performance of the proposed methods. (C) 2003 Published by Elsevier B.V.
Publisher
ELSEVIER SCIENCE BV
Issue Date
2004-03
Language
English
Article Type
Article
Citation

STATISTICS & PROBABILITY LETTERS, v.66, no.4, pp.435 - 448

ISSN
0167-7152
DOI
10.1016/j.spl.2003.08.019
URI
http://hdl.handle.net/10203/285768
Appears in Collection
MA-Journal Papers(저널논문)
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