A Note on the Nonparametric Estimation of the Conditional Mode by Wavelet Methods

A Note on the Nonparametric Estimation of the Conditional Mode by Wavelet Methods

The purpose of this note is to introduce and investigate the nonparametric estimation of the conditional mode using wavelet methods. We propose a new linear wavelet estimator for this problem. The estimator is constructed by combining a specific ratio technique and an established wavelet estimation...

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Bibliographic Details
Main Authors: Salim Bouzebda, Christophe Chesneau
Format: Article
Language:English
Published: MDPI AG 2020-10-01
Series:Stats
Subjects:
conditional mode estimation
strong consistency
nonparametric estimation
wavelet estimation
Online Access:https://www.mdpi.com/2571-905X/3/4/30
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spelling doaj-d037c92433784af1b9d72db2e5869e892020-11-25T04:08:11ZengMDPI AGStats2571-905X2020-10-0133047548310.3390/stats3040030A Note on the Nonparametric Estimation of the Conditional Mode by Wavelet MethodsSalim Bouzebda0Christophe Chesneau1Alliance Sorbonne Université, L.M.A.C., Université de Technologie de Compiègne, 60159 Compiègne, FranceDepartment of Mathematics, Université de Caen, LMNO, Campus II, Science 3, 14032 Caen, FranceThe purpose of this note is to introduce and investigate the nonparametric estimation of the conditional mode using wavelet methods. We propose a new linear wavelet estimator for this problem. The estimator is constructed by combining a specific ratio technique and an established wavelet estimation method. We obtain rates of almost sure convergence over compact subsets of <inline-formula><math display="inline"><semantics><msup><mi mathvariant="double-struck">R</mi><mi>d</mi></msup></semantics></math></inline-formula>. A general estimator beyond the wavelet methodology is also proposed, discussing adaptivity within this statistical framework.https://www.mdpi.com/2571-905X/3/4/30conditional mode estimationstrong consistencynonparametric estimationwavelet estimation
collection DOAJ
language English
format Article
sources DOAJ
author Salim Bouzebda
Christophe Chesneau
spellingShingle Salim Bouzebda
Christophe Chesneau
A Note on the Nonparametric Estimation of the Conditional Mode by Wavelet Methods
Stats
conditional mode estimation
strong consistency
nonparametric estimation
wavelet estimation
author_facet Salim Bouzebda
Christophe Chesneau
author_sort Salim Bouzebda
title A Note on the Nonparametric Estimation of the Conditional Mode by Wavelet Methods
title_short A Note on the Nonparametric Estimation of the Conditional Mode by Wavelet Methods
title_full A Note on the Nonparametric Estimation of the Conditional Mode by Wavelet Methods
title_fullStr A Note on the Nonparametric Estimation of the Conditional Mode by Wavelet Methods
title_full_unstemmed A Note on the Nonparametric Estimation of the Conditional Mode by Wavelet Methods
title_sort note on the nonparametric estimation of the conditional mode by wavelet methods
publisher MDPI AG
series Stats
issn 2571-905X
publishDate 2020-10-01
description The purpose of this note is to introduce and investigate the nonparametric estimation of the conditional mode using wavelet methods. We propose a new linear wavelet estimator for this problem. The estimator is constructed by combining a specific ratio technique and an established wavelet estimation method. We obtain rates of almost sure convergence over compact subsets of <inline-formula><math display="inline"><semantics><msup><mi mathvariant="double-struck">R</mi><mi>d</mi></msup></semantics></math></inline-formula>. A general estimator beyond the wavelet methodology is also proposed, discussing adaptivity within this statistical framework.
topic conditional mode estimation
strong consistency
nonparametric estimation
wavelet estimation
url https://www.mdpi.com/2571-905X/3/4/30
work_keys_str_mv AT salimbouzebda anoteonthenonparametricestimationoftheconditionalmodebywaveletmethods
AT christophechesneau anoteonthenonparametricestimationoftheconditionalmodebywaveletmethods
AT salimbouzebda noteonthenonparametricestimationoftheconditionalmodebywaveletmethods
AT christophechesneau noteonthenonparametricestimationoftheconditionalmodebywaveletmethods
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