Large and moderate deviation principles for nonparametric recursive kernel distribution estimators defined by stochastic approximation method

Large and moderate deviation principles for nonparametric recursive kernel distribution estimators defined by stochastic approximation method

In this paper we prove large and moderate deviations principles for the recursive kernel estimators of a distribution function defined by the stochastic approximation algorithm. We show that the estimator constructed using the stepsize which minimize the Mean Integrated Squared Error (MISE) of the c...

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Main Author: Yousri Slaoui
Format: Article
Language:English
Published: AGH Univeristy of Science and Technology Press 2019-01-01
Series:Opuscula Mathematica
Subjects:
distribution estimation
stochastic approximation algorithm
large and moderate deviations principles
Online Access:https://www.opuscula.agh.edu.pl/vol39/5/art/opuscula_math_3941.pdf
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spelling doaj-05c2114e70f44ed588ac0c0abc0fd4fe2020-11-25T02:07:54ZengAGH Univeristy of Science and Technology PressOpuscula Mathematica1232-92742019-01-01395733746https://doi.org/10.7494/OpMath.2019.39.5.7333941Large and moderate deviation principles for nonparametric recursive kernel distribution estimators defined by stochastic approximation methodYousri Slaoui0https://orcid.org/0000-0001-5295-3311University of Poitiers, Laboratoire de Mathématiques et Applications, UMR 7348 du CNRS, Téléport 2 - BP 30179, 11 Boulevard Marie et Pierre Curie, 86962 Futuroscope Chasseneuil, FranceIn this paper we prove large and moderate deviations principles for the recursive kernel estimators of a distribution function defined by the stochastic approximation algorithm. We show that the estimator constructed using the stepsize which minimize the Mean Integrated Squared Error (MISE) of the class of the recursive estimators defined by Mokkadem et al. gives the same pointwise large deviations principle (LDP) and moderate deviations principle (MDP) as the Nadaraya kernel distribution estimator.https://www.opuscula.agh.edu.pl/vol39/5/art/opuscula_math_3941.pdfdistribution estimationstochastic approximation algorithmlarge and moderate deviations principles
collection DOAJ
language English
format Article
sources DOAJ
author Yousri Slaoui
spellingShingle Yousri Slaoui
Large and moderate deviation principles for nonparametric recursive kernel distribution estimators defined by stochastic approximation method
Opuscula Mathematica
distribution estimation
stochastic approximation algorithm
large and moderate deviations principles
author_facet Yousri Slaoui
author_sort Yousri Slaoui
title Large and moderate deviation principles for nonparametric recursive kernel distribution estimators defined by stochastic approximation method
title_short Large and moderate deviation principles for nonparametric recursive kernel distribution estimators defined by stochastic approximation method
title_full Large and moderate deviation principles for nonparametric recursive kernel distribution estimators defined by stochastic approximation method
title_fullStr Large and moderate deviation principles for nonparametric recursive kernel distribution estimators defined by stochastic approximation method
title_full_unstemmed Large and moderate deviation principles for nonparametric recursive kernel distribution estimators defined by stochastic approximation method
title_sort large and moderate deviation principles for nonparametric recursive kernel distribution estimators defined by stochastic approximation method
publisher AGH Univeristy of Science and Technology Press
series Opuscula Mathematica
issn 1232-9274
publishDate 2019-01-01
description In this paper we prove large and moderate deviations principles for the recursive kernel estimators of a distribution function defined by the stochastic approximation algorithm. We show that the estimator constructed using the stepsize which minimize the Mean Integrated Squared Error (MISE) of the class of the recursive estimators defined by Mokkadem et al. gives the same pointwise large deviations principle (LDP) and moderate deviations principle (MDP) as the Nadaraya kernel distribution estimator.
topic distribution estimation
stochastic approximation algorithm
large and moderate deviations principles
url https://www.opuscula.agh.edu.pl/vol39/5/art/opuscula_math_3941.pdf
work_keys_str_mv AT yousrislaoui largeandmoderatedeviationprinciplesfornonparametricrecursivekerneldistributionestimatorsdefinedbystochasticapproximationmethod
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