IDEAS home Printed from https://ideas.repec.org/a/taf/gnstxx/v23y2011i1p67-81.html
   My bibliography  Save this article

A jump-detecting procedure based on spline estimation

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/10485250903571978
    Download Restriction: Access to full text is restricted to subscribers.

    File URL: https://libkey.io/10.1080/10485250903571978?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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. Kohler, Michael & Krzyżak, Adam, 2015. "Estimation of a jump point in random design regression," Statistics & Probability Letters, Elsevier, vol. 106(C), pages 247-255.
    3. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Irène Gijbels & Alexandre Lambert & Peihua Qiu, 2007. "Jump-Preserving Regression and Smoothing using Local Linear Fitting: A Compromise," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 59(2), pages 235-272, June.
    2. Kang, Yicheng & Shi, Yueyong & Jiao, Yuling & Li, Wendong & Xiang, Dongdong, 2021. "Fitting jump additive models," Computational Statistics & Data Analysis, Elsevier, vol. 162(C).
    3. Fan, Yanqin & Liu, Ruixuan, 2016. "A direct approach to inference in nonparametric and semiparametric quantile models," Journal of Econometrics, Elsevier, vol. 191(1), pages 196-216.
    4. Liugen Xue, 2010. "Empirical Likelihood Local Polynomial Regression Analysis of Clustered Data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 37(4), pages 644-663, December.
    5. 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.
    6. Čížek, Pavel & Koo, Chao Hui, 2021. "Jump-preserving varying-coefficient models for nonlinear time series," Econometrics and Statistics, Elsevier, vol. 19(C), pages 58-96.
    7. Youngseon Lee & Seongil Jo & Jaeyong Lee, 2022. "A variational inference for the Lévy adaptive regression with multiple kernels," Computational Statistics, Springer, vol. 37(5), pages 2493-2515, November.
    8. Gørgens, Tue, 2002. "Nonparametric comparison of regression curves by local linear fitting," Statistics & Probability Letters, Elsevier, vol. 60(1), pages 81-89, November.
    9. Čížek, Pavel & Koo, Chao Hui, 2021. "Jump-preserving varying-coefficient models for nonlinear time series," Econometrics and Statistics, Elsevier, vol. 19(C), pages 58-96.
    10. Zheng, Shuzhuan & Liu, Rong & Yang, Lijian & Härdle, Wolfgang Karl, 2014. "Simultaneous confidence corridors and variable selection for generalized additive models," SFB 649 Discussion Papers 2014-008, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    11. K. De Brabanter & Y. Liu & C. Hua, 2016. "Convergence rates for uniform confidence intervals based on local polynomial regression estimators," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 28(1), pages 31-48, March.
    12. Yu, Ping & Phillips, Peter C.B., 2018. "Threshold regression with endogeneity," Journal of Econometrics, Elsevier, vol. 203(1), pages 50-68.
    13. Gong, Xiaodong & Gao, Jiti, 2015. "Nonparametric Kernel Estimation of the Impact of Tax Policy on the Demand for Private Health Insurance in Australia," IZA Discussion Papers 9265, Institute of Labor Economics (IZA).
    14. Shih-Kang Chao & Katharina Proksch & Holger Dette & Wolfgang Karl Härdle, 2017. "Confidence Corridors for Multivariate Generalized Quantile Regression," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 35(1), pages 70-85, January.
    15. Ali Al-Sharadqah & Majid Mojirsheibani, 2020. "A simple approach to construct confidence bands for a regression function with incomplete data," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 104(1), pages 81-99, March.
    16. Chen, Gongmeng & Choi, Yoon K. & Zhou, Yong, 2008. "Detections of changes in return by a wavelet smoother with conditional heteroscedastic volatility," Journal of Econometrics, Elsevier, vol. 143(2), pages 227-262, April.
    17. Peihua Qiu, 2009. "Jump-preserving surface reconstruction from noisy data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 61(3), pages 715-751, September.
    18. Zhou, Yong & Wan, Alan T.K. & Xie, Shangyu & Wang, Xiaojing, 2010. "Wavelet analysis of change-points in a non-parametric regression with heteroscedastic variance," Journal of Econometrics, Elsevier, vol. 159(1), pages 183-201, November.
    19. Grégoire, Gérard & Hamrouni, Zouhir, 2002. "Change Point Estimation by Local Linear Smoothing," Journal of Multivariate Analysis, Elsevier, vol. 83(1), pages 56-83, October.
    20. Qiu, Peihua, 2008. "A nonparametric procedure for blind image deblurring," Computational Statistics & Data Analysis, Elsevier, vol. 52(10), pages 4828-4841, June.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:taf:gnstxx:v:23:y:2011:i:1:p:67-81. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/GNST20 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.