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Title: Large and Moderate Deviation Principles for Recursive Kernel Density Estimators Defined by Stochastic Approximation Method
Authors: Slaoui, Yousri
Keywords: Density estimation
stochastic approximation algorithm
large and moderate deviations principles
Issue Date: 2013
Publisher: Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Citation: Serdica Mathematical Journal, Vol. 39, No 1, (2013), 53p-82p
Abstract: 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.
Description: 2010 Mathematics Subject Classification: 62G07, 62L20, 60F10.
ISSN: 1310-6600
Appears in Collections:Volume 39, Number 1

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