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

Abdelkader Mokkadem (1) , Mariane Pelletier (1) , Baba Thiam (1)

1 LMV - Laboratoire de Mathématiques de Versailles

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 unidimensional 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.

Mots clés: Nadaraya-Watson estimator; Recursive kernel estimator; Large deviations principle; Moderate deviations principle

Domaines: Statistiques [math.ST]

Abdelkader Mokkadem, Mariane Pelletier, Baba Thiam. Large and moderate deviations principles for kernel estimators of the multivariate regression. 2007. ⟨hal-00136115⟩