Asymptotic results for recursive multivariate associated-kernel estimators of the probability density mass function of a data stream

Aboubacar, Amir; C Kokonendji, Célestin

doi:10.1080/03610926.2024.2360041

Article (Scientific journals)

Asymptotic results for recursive multivariate associated-kernel estimators of the probability density mass function of a data stream

Aboubacar, Amir; C Kokonendji, Célestin

2024 • In Communications in Statistics: Theory and Methods, p. 1-21

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https://hdl.handle.net/2268/324237

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10.1080/03610926.2024.2360041

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Keywords :

Asymmetric kernel; asymptotic normality; Lq-consistency; recursive estimator; strong consistency; Asymptotic normality; Asymptotic results; Data stream; Kernel estimators; Mass functions; Probability densities; Recursive estimators; Strong consistency; Statistics and Probability

Abstract :

[en] In this article, our central focus is to investigate the non parametric estimator of the probability density or mass function of a data stream by using the general family of kernels, also called multivariate associated kernels. Being able to estimate categorial, count, discrete, and (semi)continuous distributions, these multivariate associated kernel estimators unify several particular cases. Within this framework, we first introduce a recursive estimator for non classical associated kernels. Under reasonable assumptions, we subsequently exhibit their asymptotic results, such as the local uniform Lq-consistency, the pointwise asymptotic normality and finally the strong global consistency. Illustrative examples of associated kernels are revisited.

Disciplines :

Mathematics

Author, co-author :

Aboubacar, Amir ; Université de Liège - ULiège > Département de mathématique > Probabilités - Analyse stochastique

C Kokonendji, Célestin ; Laboratoire de mathématiques de Besançon, CNRS-UFC Université de Franche-Comté, Besançon cedex, France ; Laboratoire de mathématiques et connexes de Bangui, LmcB Université de Bangui, Bangui, France

Language :

English

Title :

Asymptotic results for recursive multivariate associated-kernel estimators of the probability density mass function of a data stream

Publication date :

2024

Journal title :

Communications in Statistics: Theory and Methods

ISSN :

0361-0926

eISSN :

1532-415X

Publisher :

Taylor and Francis Ltd.

Pages :

1-21

Peer reviewed :

Peer Reviewed verified by ORBi

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https://www.tandfonline.com/doi/pdf/10.1080/03610926.2024.2360041

Available on ORBi :

since 13 November 2024

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