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A jump-detecting procedure based on spline estimation

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  • Shujie Ma
  • Lijian Yang

Abstract

In a random-design nonparametric regression model, procedures for detecting jumps in the regression function via constant and linear spline estimation method are proposed based on the maximal differences of the spline estimators among neighbouring knots, the limiting distributions of which are obtained when the regression function is smooth. Simulation experiments provide strong evidence that corroborates with the asymptotic theory, while the computing is extremely fast. The detecting procedure is illustrated by analysing the thickness of pennies data set.

Suggested Citation

  • Shujie Ma & Lijian Yang, 2011. "A jump-detecting procedure based on spline estimation," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 23(1), pages 67-81.
    • Handle: RePEc:taf:gnstxx:v:23:y:2011:i:1:p:67-81
    DOI: 10.1080/10485250903571978
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    References listed on IDEAS

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    1. Qiu, Peihua, 2007. "Jump Surface Estimation, Edge Detection, and Image Restoration," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 745-756, June.
    2. Kang, Kee-Hoon & Koo, Ja-Yong & Park, Cheol-Woo, 2000. "Kernel estimation of discontinuous regression functions," Statistics & Probability Letters, Elsevier, vol. 47(3), pages 277-285, April.
    3. Müller, Hans-Georg & Song, Kai-Sheng, 1997. "Two-stage change-point estimators in smooth regression models," Statistics & Probability Letters, Elsevier, vol. 34(4), pages 323-335, June.
    4. Park, Cheol-Woo & Kim, Woo-Chul, 2004. "Estimation of a regression function with a sharp change point using boundary wavelets," Statistics & Probability Letters, Elsevier, vol. 66(4), pages 435-448, March.
    5. Härdle, Wolfgang, 1989. "Asymptotic maximal deviation of M-smoothers," Journal of Multivariate Analysis, Elsevier, vol. 29(2), pages 163-179, May.
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    Cited by:

    1. Yujiao Yang & Qiongxia Song, 2014. "Jump detection in time series nonparametric regression models: a polynomial spline approach," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 66(2), pages 325-344, April.
    2. Shujie Ma & Yanyuan Ma & Yanqing Wang & Eli S. Kravitz & Raymond J. Carroll, 2017. "A Semiparametric Single-Index Risk Score Across Populations," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(520), pages 1648-1662, October.
    3. Kohler, Michael & Krzyżak, Adam, 2015. "Estimation of a jump point in random design regression," Statistics & Probability Letters, Elsevier, vol. 106(C), pages 247-255.

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