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Wavelet Detection and Estimation of Change Points in Nonparametric Regression Models under Random Design 被引量：2

Wavelet Detection and Estimation of Change Points in Nonparametric Regression Models under Random Design
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摘要 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. 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 coeficients 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.
作者 ZHAO Wen Zhi TIAN Zheng XIA Zhi Ming
机构地区 Department of Applied Mathematics Department of Mathematics
出处 《Journal of Mathematical Research and Exposition》 CSCD 2009年第2期247-256,共10页 数学研究与评论（英文版）
基金 the National Natural Science Foundation of China （No. 60375003） the Astronautics Basal Science Foundation of China （No. 03153059）.
关键词 random design nonparametric regression model change point wavelet transformation consistent test rate of convergence. 随机设计 非参数回归模型 变点 小波 检测 估计
分类号 O212.7 [理学—概率论与数理统计]
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参考文献8

  • 1MULLER H. Change-points in nanpararnetric regression analysis [J]. Ann. Statist., 1992, 20(2): 737-761.
  • 2RAIMONDO M, TAJVIDI N. A peaks over threshold model for change-point detection by wavelets [J]. Statist. Sinica, 2004, 14(2): 395-412.
  • 3WANG Yazhen. Jump and sharp cusp detection by wavelets [J]. Biometrika, 1995, 82(2): 385-397.
  • 4ODGEN T, PARZEN O. Change-point approach to data analytic thresholding [J]. Statist. Comput., 1996, 6: 93-99.
  • 5RAIMONDO M. Minimax estimation of sharp change points [J]. Ann. Statist., 1998, 26(4): 1379-1397.
  • 6ANTONIADIS A, GIJBELS I. Detecting abrupt changes by-wavelet methods [J]. J. Nonparametr. Star., 2002, 14(1-2): 7-29.
  • 7HARDLE W, KERKYACHARIAN G, PICARD D. et al. Wavelets, Approximation, and Statistical Applications [M]. Springer-Verlag, New York, 1998.
  • 8PETROV V. Sums of Independent Random Variables [M]. Springer-Verlag, New York-Heidelberg, 1975.

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Journal of Mathematical Research and Exposition
2009年 第2期

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