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Kernel estimation of discontinuous regression functions

Author

Listed:
  • Kang, Kee-Hoon
  • Koo, Ja-Yong
  • Park, Cheol-Woo

Abstract

A kernel regression estimator is proposed wherein the regression function is smooth, except possibly for a finite number of points of discontinuity. The proposed estimator uses preliminary estimators for the location and size of discontinuities or change-points in an otherwise smooth regression model and then uses an ordinary kernel regression estimator based on suitably adjusted data. Global L2 rates of convergence of curve estimates are derived. It is shown that these rates of convergence are the same as those for ordinary kernel regression estimators of smooth curves. Moreover, pointwise asymptotic normality is also obtained. The finite-sample performance of the proposed method is illustrated by simulated examples.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:47:y:2000:i:3:p:277-285
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    Citations

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    Cited by:

    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. 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.
    3. 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.
    4. 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.
    5. 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.
    6. Kang, Yicheng & Shi, Yueyong & Jiao, Yuling & Li, Wendong & Xiang, Dongdong, 2021. "Fitting jump additive models," Computational Statistics & Data Analysis, Elsevier, vol. 162(C).
    7. Koo, Chao, 2018. "Essays on functional coefficient models," Other publications TiSEM ba87b8a5-3c55-40ec-967d-9, Tilburg University, School of Economics and Management.
    8. 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.
    9. 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.

    More about this item

    Keywords

    Boundary kernel Change-points Jump location Jump size L2 convergence Rate of convergence Weak convergence;

    JEL classification:

    • L2 - Industrial Organization - - Firm Objectives, Organization, and Behavior

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