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Large and moderate deviations principles for kernel estimators of the multivariate regression

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Abstract

In this paper, we prove large deviations principle for the Nadaraya-Watson estimator and for the semi-recursive kernel estimator of the regression in the multidimensional case. Under suitable conditions, we show that the rate function is a good rate function. We thus generalize the results already obtained in the one-dimensional case for the Nadaraya-Watson estimator. Moreover, we give a moderate deviations principle for these two estimators. It turns out that the rate function obtained in the moderate deviations principle for the semi-recursive estimator is larger than the one obtained for the Nadaraya-Watson estimator.

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Authors and Affiliations

  1. Dépt. de Mathématiques, Univ. de Versailles-Saint-Quentin, Versailles, France

    A. Mokkadem, M. Pelletier & B. Thiam

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  1. A. Mokkadem
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  2. M. Pelletier
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  3. B. Thiam
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Correspondence to A. Mokkadem.

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Mokkadem, A., Pelletier, M. & Thiam, B. Large and moderate deviations principles for kernel estimators of the multivariate regression. Math. Meth. Stat. 17, 146–172 (2008). https://doi.org/10.3103/S1066530708020051

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  • DOI: https://doi.org/10.3103/S1066530708020051

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