IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v66y2004i4p435-448.html
   My bibliography  Save this article

Estimation of a regression function with a sharp change point using boundary wavelets

Author

Listed:
  • Park, Cheol-Woo
  • Kim, Woo-Chul

Abstract

We propose a sharp change point estimator based on the differences between right and left boundary wavelet smoothers. It is constructed by applying a two-step procedure to the observed data and has the minimax convergence rate. Next, we estimate the regression function with boundary wavelets in the left and right regions of the estimated jump point separately. This method helps us to capture the feature of a discontinuity in practice. Both mean integrated squared error and mean squared error of the estimated function are derived and we then show that these rates of convergence are the same as the case in which a jump point does not exist. Simulated examples demonstrate the improved performance of the proposed methods.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:66:y:2004:i:4:p:435-448
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-7152(03)00365-1
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    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. 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.
    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. Li, Zheng & Zeng, Jingjing & Hensher, David A., 2023. "An efficient approach to structural breaks and the case of automobile gasoline consumption in Australia," Transportation Research Part A: Policy and Practice, Elsevier, vol. 169(C).
    2. 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.
    3. 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.

    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. 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.
    2. 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.
    3. Xiaodong Gong & Jiti Gao, 2015. "Nonparametric Kernel Estimation of the Impact of Tax Policy on the Demand for Private Health Insurance in Australia," Monash Econometrics and Business Statistics Working Papers 6/15, Monash University, Department of Econometrics and Business Statistics.
    4. 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.
    5. 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.
    6. Koo, Chao, 2018. "Essays on functional coefficient models," Other publications TiSEM ba87b8a5-3c55-40ec-967d-9, Tilburg University, School of Economics and Management.
    7. Kang, Yicheng & Shi, Yueyong & Jiao, Yuling & Li, Wendong & Xiang, Dongdong, 2021. "Fitting jump additive models," Computational Statistics & Data Analysis, Elsevier, vol. 162(C).
    8. I. Sánchez-Borrego & M. Martínez-Miranda & A. González-Carmona, 2006. "Local linear kernel estimation of the discontinuous regression function," Computational Statistics, Springer, vol. 21(3), pages 557-569, December.

    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:eee:stapro:v:66:y:2004:i:4:p:435-448. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    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.