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Robust estimation for nonparametric generalized regression

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  • Bianco, Ana M.
  • Boente, Graciela
  • Sombielle, Susana

Abstract

This paper focuses on nonparametric regression estimation for the parameters of a discrete or continuous distribution, such as the Poisson or Gamma distributions, when anomalous data are present. The proposal is a natural extension of robust methods developed in the setting of parametric generalized linear models. Robust estimators bounding either large values of the deviance or of the Pearson residuals are introduced and their asymptotic behaviour is derived. Through a Monte Carlo study, for the Poisson and Gamma distributions, the finite properties of the proposed procedures are investigated and their performance is compared with that of the classical ones. A resistant cross-validation method to choose the smoothing parameter is also considered.

Suggested Citation

  • Bianco, Ana M. & Boente, Graciela & Sombielle, Susana, 2011. "Robust estimation for nonparametric generalized regression," Statistics & Probability Letters, Elsevier, vol. 81(12), pages 1986-1994.
    • Handle: RePEc:eee:stapro:v:81:y:2011:i:12:p:1986-1994
    DOI: 10.1016/j.spl.2011.08.007
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    References listed on IDEAS

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    1. Boente, Graciela & Fraiman, Ricardo, 1989. "Robust nonparametric regression estimation," Journal of Multivariate Analysis, Elsevier, vol. 29(2), pages 180-198, May.
    2. Georgiev, Alexander A., 1988. "Consistent nonparametric multiple regression: The fixed design case," Journal of Multivariate Analysis, Elsevier, vol. 25(1), pages 100-110, April.
    3. Härdle, Wolfgang, 1984. "Robust regression function estimation," Journal of Multivariate Analysis, Elsevier, vol. 14(2), pages 169-180, April.
    4. Cantoni E. & Ronchetti E., 2001. "Robust Inference for Generalized Linear Models," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1022-1030, September.
    5. J. B. Copas, 1983. "Plotting p Against X," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 32(1), pages 25-31, March.
    6. Croux, Christophe & Haesbroeck, Gentiane, 2003. "Implementing the Bianco and Yohai estimator for logistic regression," Computational Statistics & Data Analysis, Elsevier, vol. 44(1-2), pages 273-295, October.
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    Cited by:

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    3. Zhao, Ge & Ma, Yanyuan, 2016. "Robust nonparametric kernel regression estimator," Statistics & Probability Letters, Elsevier, vol. 116(C), pages 72-79.

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