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The wavelet identification for jump points of derivative in regression model

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  • Luan, Yihui
  • Xie, Zhongjie

Abstract

A method is proposed to detect the number, locations and heights of jump points of the derivative in the regressive model [eta]i=f([xi]i)+[var epsilon]i, by checking if the empirical indirect wavelet coefficients of data have significantly large absolute values across fine scale levels. The consistency of the estimators is established and practical implementation is discussed. Some simulation examples are given to test our method.

Suggested Citation

  • Luan, Yihui & Xie, Zhongjie, 2001. "The wavelet identification for jump points of derivative in regression model," Statistics & Probability Letters, Elsevier, vol. 53(2), pages 167-180, June.
    • Handle: RePEc:eee:stapro:v:53:y:2001:i:2:p:167-180
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    References listed on IDEAS

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    1. Ogden, Todd & Parzen, Emanuel, 1996. "Data dependent wavelet thresholding in nonparametric regression with change-point applications," Computational Statistics & Data Analysis, Elsevier, vol. 22(1), pages 53-70, June.
    2. Iain M. Johnstone & Bernard W. Silverman, 1997. "Wavelet Threshold Estimators for Data with Correlated Noise," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 59(2), pages 319-351.
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