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Adaptive estimators for nonparametric heteroscedastic regression models

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  • J.-Y. Brua

Abstract

This paper deals with the estimation of a regression function at a fixed point in nonparametric heteroscedastic regression models with Gaussian noise. We assume that the variance of the noise depends on the regressor and on the regression function. We make use of the minimax absolute error risk taken over a Hölder class of regression functions. As the smoothness of the regression function is supposed to be unknown, we construct an adaptive kernel estimator which attains the minimax rate. More precisely, we give an asymptotic upper bound and an asymptotic lower bound for the minimax risk.

Suggested Citation

  • J.-Y. Brua, 2009. "Adaptive estimators for nonparametric heteroscedastic regression models," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 21(8), pages 991-1002.
    • Handle: RePEc:taf:gnstxx:v:21:y:2009:i:8:p:991-1002
    DOI: 10.1080/10485250902993645
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    References listed on IDEAS

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    1. Galtchouk, L. & Pergamenshchikov, S., 2006. "Asymptotically efficient estimates for nonparametric regression models," Statistics & Probability Letters, Elsevier, vol. 76(8), pages 852-860, April.
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