Location and Size of the Mode Nonparametric Estimation Stochastic Approximation Algorithms Averaging Principle
Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Serdica Mathematical Journal, Vol. 34, No 3, (2008), 651p-688p
Tsybakov  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).