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Estimation of regression functions with a discontinuity in a derivative with local polynomial fits

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  • Huh, J.
  • Carrière, K. C.

Abstract

We consider an estimation strategy for regression functions which may have discontinuity/change point in the derivative functions at an unknown location. First, we propose methods of estimation for the location and the jump size of the change point via the local polynomial fitting based on a kernel weighted method. The estimated location of the change point will be shown to achieve the asymptotic minimax rate of convergence of n-1/(2[nu]+1), where [nu] is the degree of the derivative. Next, using the data sets split by the estimated location of the change point, we estimate their respective regression functions. Global Lp rate of convergence of the estimated regression function is derived. Computer simulation will demonstrate the improved performance of the proposed methods over the existing ones.

Suggested Citation

  • Huh, J. & Carrière, K. C., 2002. "Estimation of regression functions with a discontinuity in a derivative with local polynomial fits," Statistics & Probability Letters, Elsevier, vol. 56(3), pages 329-343, February.
    • Handle: RePEc:eee:stapro:v:56:y:2002:i:3:p:329-343
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    References listed on IDEAS

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    1. 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.
    2. Irene Gijbels & Peter Hall & Aloïs Kneip, 1999. "On the Estimation of Jump Points in Smooth Curves," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 51(2), pages 231-251, June.
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    Cited by:

    1. Huh, Jib, 2010. "Detection of a change point based on local-likelihood," Journal of Multivariate Analysis, Elsevier, vol. 101(7), pages 1681-1700, August.
    2. Huh, Jib, 2012. "Nonparametric estimation of the regression function having a change point in generalized linear models," Statistics & Probability Letters, Elsevier, vol. 82(4), pages 843-851.
    3. Jens Klotsche & Andrew T. Gloster, 2012. "Estimating a Meaningful Point of Change," Journal of Educational and Behavioral Statistics, , vol. 37(5), pages 579-600, October.

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