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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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    Citations

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    Cited by:

    1. 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.
    2. 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.
    3. Omar Fetitah & Mohammed Kadi Attouch & Salah Khardani & Ali Righi, 2023. "Robust nonparametric equivariant regression for functional data with responses missing at random," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 86(8), pages 899-929, November.
    4. Bianco, Ana M. & Spano, Paula M., 2017. "Robust estimation in partially linear errors-in-variables models," Computational Statistics & Data Analysis, Elsevier, vol. 106(C), pages 46-64.
    5. Lee, Myoung-jae & Melenberg, Bertrand, 1998. "Bounding quantiles in sample selection models," Economics Letters, Elsevier, vol. 61(1), pages 29-35, October.
    6. Guillermo Henry & Daniela Rodriguez, 2009. "Robust nonparametric regression on Riemannian manifolds," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 21(5), pages 611-628.
    7. Bianco, Ana M. & Boente, Graciela & Sombielle, Susana, 2011. "Robust estimation for nonparametric generalized regression," Statistics & Probability Letters, Elsevier, vol. 81(12), pages 1986-1994.
    8. 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.
    9. Lin, Min-Bin & Wang, Bingling & Bocart, Fabian Y.R.P. & Hafner, Christian M. & Härdle, Wolfgang K., 2022. "DAI Digital Art Index : a robust price index for heterogeneous digital assets," LIDAM Discussion Papers ISBA 2022036, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    10. 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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