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

Djeddour, Khédidja; Mokkadem, Abdelkader; Pelletier, Mariane

Serdica Mathematical Journal (2008)

- Volume: 34, Issue: 3, page 651-688
- ISSN: 1310-6600

## Access Full Article

top## Abstract

top## How to cite

topDjeddour, 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 -

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.