Estimation of regression functions with a discontinuity in a derivative with local polynomial fits
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.
Volume (Year): 56 (2002)
Issue (Month): 3 (February)
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- 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.
- 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.
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