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Nonparametric estimation of the regression function having a change point in generalized linear models

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  • Huh, Jib

Abstract

In this paper, the local polynomial fit based on the kernel weighted local-likelihood function and the location of the change point is considered as an estimator for the regression function or its νth derivative. Using the data sets split by the location, we estimate the left and right parts of the regression function or its νth derivative. The global L2 rate of convergence of the estimated function is derived. The finite-sample performances of the proposed estimators are illustrated using simulated and real examples.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:82:y:2012:i:4:p:843-851
    DOI: 10.1016/j.spl.2012.01.009
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    References listed on IDEAS

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    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. Huh, J. & Park, B. U., 2002. "Likelihood-Based Local Polynomial Fitting for Single-Index Models," Journal of Multivariate Analysis, Elsevier, vol. 80(2), pages 302-321, February.
    3. Grégoire, Gérard & Hamrouni, Zouhir, 2002. "Change Point Estimation by Local Linear Smoothing," Journal of Multivariate Analysis, Elsevier, vol. 83(1), pages 56-83, October.
    4. Huh, Jib, 2010. "Detection of a change point based on local-likelihood," Journal of Multivariate Analysis, Elsevier, vol. 101(7), pages 1681-1700, August.
    5. 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.
    6. Pollard, David, 1991. "Asymptotics for Least Absolute Deviation Regression Estimators," Econometric Theory, Cambridge University Press, vol. 7(2), pages 186-199, June.
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