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Robust regression function estimation

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  • Härdle, Wolfgang

Abstract

A robust estimator of the regression function is proposed combining kernel methods as introduced for density estimation and robust location estimation techniques. Weak and strong consistency and asymptotic normality are shown under mild conditions on the kernel sequence. The asymptotic variance is a product from a factor depending only on the kernel and a factor similar to the asymptotic variance in robust estimation of location. The estimation is minimax robust in the sense of [7]. Robust estimation of a location parameter. Ann. Math. Statist.33 73-101.

Suggested Citation

  • Härdle, Wolfgang, 1984. "Robust regression function estimation," Journal of Multivariate Analysis, Elsevier, vol. 14(2), pages 169-180, April.
  • Handle: RePEc:eee:jmvana:v:14:y:1984:i:2:p:169-180
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    Cited by:

    1. Bianco, Ana M. & Boente, Graciela & Sombielle, Susana, 2011. "Robust estimation for nonparametric generalized regression," Statistics & Probability Letters, Elsevier, vol. 81(12), pages 1986-1994.
    2. Vazquez-Alvarez, R. & Melenberg, B. & van Soest, A.H.O., 1999. "Nonparametric Bounds on the Income Distribution in the Presence of Item Nonresponse," Discussion Paper 1999-33, Tilburg University, Center for Economic Research.
    3. Lee, Myoung-jae & Melenberg, Bertrand, 1998. "Bounding quantiles in sample selection models," Economics Letters, Elsevier, vol. 61(1), pages 29-35, October.
    4. Chen, Jia & Li, Degui & Zhang, Lixin, 2010. "Robust estimation in a nonlinear cointegration model," Journal of Multivariate Analysis, Elsevier, vol. 101(3), pages 706-717, March.
    5. Ostap Okhrin & Stefan Trück, 2015. "Editorial to the special issue on Applicable semiparametrics of computational statistics," Computational Statistics, Springer, vol. 30(3), pages 641-646, September.
    6. Robinson, P. M., 1995. "The approximate distribution of nonparametric regression estimates," Statistics & Probability Letters, Elsevier, vol. 23(2), pages 193-201, May.

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