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

Abdelkader Mokkadem; Mariane Pelletier; Baba Thiam

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

Abdelkader Mokkadem·Mariane Pelletier·Baba Thiam

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Abstract

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.

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Abdelkader Mokkadem, Mariane Pelletier, Baba Thiam. 2006-01-18. Large and moderate deviations principles for recursive kernel estimators of a multivariate density and its partial derivatives. https://arxiv.org/abs/math/0601429

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