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On a robust local estimator for the scale function in heteroscedastic nonparametric regression

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  • Boente, Graciela
  • Ruiz, Marcelo
  • Zamar, Ruben H.

Abstract

When the data used to fit an heteroscedastic nonparametric regression model are contaminated with outliers, robust estimators of the scale function are needed in order to obtain robust estimators of the regression function and to construct robust confidence bands. In this paper, local M-estimators of the scale function based on consecutive differences of the responses, for fixed designs are considered. Under mild regularity conditions, the asymptotic behavior of the local M-estimators for general weight functions is derived.

Suggested Citation

  • Boente, Graciela & Ruiz, Marcelo & Zamar, Ruben H., 2010. "On a robust local estimator for the scale function in heteroscedastic nonparametric regression," Statistics & Probability Letters, Elsevier, vol. 80(15-16), pages 1185-1195, August.
    • Handle: RePEc:eee:stapro:v:80:y:2010:i:15-16:p:1185-1195
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    References listed on IDEAS

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    1. Holger Dette & Benjamin Hetzler, 2009. "A simple test for the parametric form of the variance function in nonparametric regression," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 61(4), pages 861-886, December.
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    4. Levine, M., 2006. "Bandwidth selection for a class of difference-based variance estimators in the nonparametric regression: A possible approach," Computational Statistics & Data Analysis, Elsevier, vol. 50(12), pages 3405-3431, August.
    5. Boente, Graciela & Rodriguez, Daniela, 2008. "Robust bandwidth selection in semiparametric partly linear regression models: Monte Carlo study and influential analysis," Computational Statistics & Data Analysis, Elsevier, vol. 52(5), pages 2808-2828, January.
    6. Caliskan, Derya & Croux, Christophe & Gelper, Sarah, 2009. "Efficient and robust scale estimation for trended time series," Statistics & Probability Letters, Elsevier, vol. 79(18), pages 1900-1905, September.
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    Cited by:

    1. Boente, Graciela & Ruiz, Marcelo & Zamar, Ruben H., 2012. "Bandwidth choice for robust nonparametric scale function estimation," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1594-1608.

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