Large and moderate deviations principles for recursive kernel estimators of a multivariate density and its partial derivatives.

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

1 LMV - Laboratoire de Mathématiques de Versailles

In this paper we prove large and moderate deviations principles for the recursive kernel estimator of a probability density function and its partial derivatives. Unlike the density estimator, the derivatives estimators exhibit a quadratic behavior not only for the moderate deviations scale but also for the large deviations one. We provide results both for the pointwise and the uniform deviations.

Mots clés: Multivariate recursive kernel estimation of a density and its derivatives; Large and moderate deviations principles

Domaines: Statistiques [math.ST]

Abdelkader Mokkadem, Mariane Pelletier, Baba Thiam. Large and moderate deviations principles for recursive kernel estimators of a multivariate density and its partial derivatives.. 2006. ⟨hal-00017207⟩