Geodesic
Large and Moderate Deviation Principles for Recursive Kernel Density Estimators Defined by Stochastic Approximation Method
Serdica Mathematical Journal, Tome 39 (2013) no. 1, pp. 53-82.

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In this paper we prove large and moderate deviations principles for the recursive kernel estimators of a probability density function defined by the stochastic approximation algorithm introduced by Mokkadem et al.([10]. The stochastic approximation method for the estimation of a probability density. J. Statist. Plann. Inference 139 (2009), 2459–2478). We show that the estimator constructed using the stepsize which minimize the variance of the class of the recursive estimators defined in [10] gives the same pointwise LDP and MDP as the Rosenblatt kernel estimator. We provide results both for the pointwise and the uniform deviations.
Keywords: Density estimation, stochastic approximation algorithm, large and moderate deviations principles 
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     author = {Slaoui, Yousri},
     title = {Large and {Moderate} {Deviation} {Principles} for {Recursive} {Kernel} {Density} {Estimators} {Defined} by {Stochastic} {Approximation} {Method}},
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Slaoui, Yousri. Large and Moderate Deviation Principles for Recursive Kernel Density Estimators Defined by Stochastic Approximation Method. Serdica Mathematical Journal, Tome 39 (2013) no. 1, pp. 53-82. http://geodesic.mathdoc.fr/item/SMJ2_2013_39_1_a3/