Wavelet Detection and Estimation of Change Points in Nonparametric Regression Models under Random Design
Received:June 22, 2007  Revised:November 22, 2007
Key Words: random design   nonparametric regression model   change point   wavelet transformation   consistent test   rate of convergence.  
Fund Project:the National Natural Science Foundation of China (No.60375003); the Astronautics Basal Science Foundation of China (No.03I53059).
Author NameAffiliation
ZHAO Wen Zhi Department of Applied Mathematics, Northwestern Polytechnical University, Shaanxi 710072, China 
TIAN Zheng Department of Applied Mathematics, Northwestern Polytechnical University, Shaanxi 710072, China 
XIA Zhi Ming Department of Mathematics, Northwest University, Shaanxi 710069, China 
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Abstract:
      A wavelet method of detection and estimation of change points in nonparametric regression models under random design is proposed. The confidence bound of our test is derived by using the test statistics based on empirical wavelet coefficients as obtained by wavelet transformation of the data which is observed with noise. Moreover, the consistence of the test is proved while the rate of convergence is given. The method turns out to be effective after being tested on simulated examples and applied to IBM stock market data.
Citation:
DOI:10.3770/j.issn:1000-341X.2009.02.007
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