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.

Voir la notice de l'article provenant de la source Bulgarian Digital Mathematics Library

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 
@article{SMJ2_2008_34_3_a8,
     author = {Djeddour, Kh\'edidja and Mokkadem, Abdelkader and Pelletier, Mariane},
     title = {On the {Recursive} {Estimation} of the {Location} and of the {Size} of the {Mode} of a {Probability} {Density}},
     journal = {Serdica Mathematical Journal},
     pages = {651--688},
     publisher = {mathdoc},
     volume = {34},
     number = {3},
     year = {2008},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SMJ2_2008_34_3_a8/}
}
TY  - JOUR
AU  - Djeddour, Khédidja
AU  - Mokkadem, Abdelkader
AU  - Pelletier, Mariane
TI  - On the Recursive Estimation of the Location and of the Size of the Mode of a Probability Density
JO  - Serdica Mathematical Journal
PY  - 2008
SP  - 651
EP  - 688
VL  - 34
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SMJ2_2008_34_3_a8/
LA  - en
ID  - SMJ2_2008_34_3_a8
ER  - 
%0 Journal Article
%A Djeddour, Khédidja
%A Mokkadem, Abdelkader
%A Pelletier, Mariane
%T On the Recursive Estimation of the Location and of the Size of the Mode of a Probability Density
%J Serdica Mathematical Journal
%D 2008
%P 651-688
%V 34
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SMJ2_2008_34_3_a8/
%G en
%F SMJ2_2008_34_3_a8
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/