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Title: On the Recursive Estimation of the Location and of the Size of the Mode of a Probability Density
Authors: Djeddour, Khédidja
Mokkadem, Abdelkader
Pelletier, Mariane
Keywords: Location and Size of the Mode
Nonparametric Estimation
Stochastic Approximation Algorithms
Averaging 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.
ISSN: 1310-6600
Appears in Collections:Volume 34, Number 3

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