Please use this identifier to cite or link to this item: http://hdl.handle.net/10525/2621

 Title: On the Recursive Estimation of the Location and of the Size of the Mode of a Probability Density Authors: Djeddour, KhédidjaMokkadem, AbdelkaderPelletier, Mariane Keywords: Location and Size of the ModeNonparametric EstimationStochastic Approximation AlgorithmsAveraging Principle Issue Date: 2008 Publisher: Institute of Mathematics and Informatics Bulgarian Academy of Sciences Citation: Serdica Mathematical Journal, Vol. 34, No 3, (2008), 651p-688p Abstract: Tsybakov [31] introduced the method of stochastic approximation to construct a recursive estimator of the location q of the mode of a probability density. The aim of this paper is to provide a companion algorithm to Tsybakov's algorithm, which allows to simultaneously recursively approximate the size m of the mode. We provide a precise study of the joint weak convergence rate of both estimators. Moreover, we introduce the averaging principle of stochastic approximation algorithms to construct asymptotically efficient algorithms approximating the couple (q,m). Description: 2000 Mathematics Subject Classification: 62G07, 62L20. URI: http://hdl.handle.net/10525/2621 ISSN: 1310-6600 Appears in Collections: Volume 34, Number 3

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