Geodesic
Large and Moderate Deviations Principles for Recursive Kernel Estimator of a Multivariate Density and its Partial Derivatives
Serdica Mathematical Journal, Tome 32 (2006) no. 4, pp. 323-354.

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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 behaviour 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.
Keywords: Kernel Estimation, Derivatives, Deviations Principles 
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     title = {Large and {Moderate} {Deviations} {Principles} for {Recursive} {Kernel} {Estimator} of a {Multivariate} {Density} and its {Partial} {Derivatives}},
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Mokkadem, Abdelkader; Mariane, Pelletier; Baba, Thiam. Large and Moderate Deviations Principles for Recursive Kernel Estimator of a Multivariate Density and its Partial Derivatives. Serdica Mathematical Journal, Tome 32 (2006) no. 4, pp. 323-354. http://geodesic.mathdoc.fr/item/SMJ2_2006_32_4_a3/