Geodesic
On the Recursive Estimation of the Location and of the Size of the Mode of a Probability Density
Serdica Mathematical Journal, Tome 34 (2008) no. 3, pp. 651-688

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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).
Keywords: Location and Size of the Mode, Nonparametric Estimation, Stochastic Approximation Algorithms, Averaging Principle 
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Djeddour, Khédidja; Mokkadem, Abdelkader; Pelletier, Mariane. On the Recursive Estimation of the Location and of the Size of the Mode of a Probability Density. Serdica Mathematical Journal, Tome 34 (2008) no. 3, pp. 651-688. http://geodesic.mathdoc.fr/item/SMJ2_2008_34_3_a8/