On the Recursive Estimation of the Location and of the Size of the Mode of a Probability Density

Djeddour, Khédidja, Mokkadem, Abdelkader, and Pelletier, Mariane. "On the Recursive Estimation of the Location and of the Size of the Mode of a Probability Density." Serdica Mathematical Journal 34.3 (2008): 651-688. <http://eudml.org/doc/281450>.

@article{Djeddour2008,
abstract = {2000 Mathematics Subject Classification: 62G07, 62L20.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).},
author = {Djeddour, Khédidja, Mokkadem, Abdelkader, Pelletier, Mariane},
journal = {Serdica Mathematical Journal},
keywords = {Location and Size of the Mode; Nonparametric Estimation; Stochastic Approximation Algorithms; Averaging Principle; nonparametric estimation; stochastic approximation algorithms; averaging principle},
language = {eng},
number = {3},
pages = {651-688},
publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},
title = {On the Recursive Estimation of the Location and of the Size of the Mode of a Probability Density},
url = {http://eudml.org/doc/281450},
volume = {34},
year = {2008},
}

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
PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences
VL - 34
IS - 3
SP - 651
EP - 688
AB - 2000 Mathematics Subject Classification: 62G07, 62L20.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).
LA - eng
KW - Location and Size of the Mode; Nonparametric Estimation; Stochastic Approximation Algorithms; Averaging Principle; nonparametric estimation; stochastic approximation algorithms; averaging principle
UR - http://eudml.org/doc/281450
ER -