A General Result on the Mean Integrated Squared Error of the Hard Thresholding Wavelet Estimator under α-Mixing Dependence

A General Result on the Mean Integrated Squared Error of the Hard Thresholding Wavelet Estimator under α-Mixing Dependence

We consider the estimation of an unknown function f for weakly dependent data (α-mixing) in a general setting. Our contribution is theoretical: we prove that a hard thresholding wavelet estimator attains a sharp rate of convergence under the mean integrated squared error (MISE) over Besov balls with...

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Main Author: Christophe Chesneau
Format: Article
Language:English
Published: Hindawi Limited 2014-01-01
Series:Journal of Probability and Statistics
Online Access:http://dx.doi.org/10.1155/2014/403764
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spelling doaj-032bf678aa104bb98573247f5ff36ad12020-11-25T00:18:39ZengHindawi LimitedJournal of Probability and Statistics1687-952X1687-95382014-01-01201410.1155/2014/403764403764A General Result on the Mean Integrated Squared Error of the Hard Thresholding Wavelet Estimator under α-Mixing DependenceChristophe Chesneau0Laboratoire de Mathéematiques Nicolas Oresme, Université de Caen, BP 5186, 14032 Caen Cedex, FranceWe consider the estimation of an unknown function f for weakly dependent data (α-mixing) in a general setting. Our contribution is theoretical: we prove that a hard thresholding wavelet estimator attains a sharp rate of convergence under the mean integrated squared error (MISE) over Besov balls without imposing too restrictive assumptions on the model. Applications are given for two types of inverse problems: the deconvolution density estimation and the density estimation in a GARCH-type model, both improve existing results in this dependent context. Another application concerns the regression model with random design.http://dx.doi.org/10.1155/2014/403764
collection DOAJ
language English
format Article
sources DOAJ
author Christophe Chesneau
spellingShingle Christophe Chesneau
A General Result on the Mean Integrated Squared Error of the Hard Thresholding Wavelet Estimator under α-Mixing Dependence
Journal of Probability and Statistics
author_facet Christophe Chesneau
author_sort Christophe Chesneau
title A General Result on the Mean Integrated Squared Error of the Hard Thresholding Wavelet Estimator under α-Mixing Dependence
title_short A General Result on the Mean Integrated Squared Error of the Hard Thresholding Wavelet Estimator under α-Mixing Dependence
title_full A General Result on the Mean Integrated Squared Error of the Hard Thresholding Wavelet Estimator under α-Mixing Dependence
title_fullStr A General Result on the Mean Integrated Squared Error of the Hard Thresholding Wavelet Estimator under α-Mixing Dependence
title_full_unstemmed A General Result on the Mean Integrated Squared Error of the Hard Thresholding Wavelet Estimator under α-Mixing Dependence
title_sort general result on the mean integrated squared error of the hard thresholding wavelet estimator under α-mixing dependence
publisher Hindawi Limited
series Journal of Probability and Statistics
issn 1687-952X
1687-9538
publishDate 2014-01-01
description We consider the estimation of an unknown function f for weakly dependent data (α-mixing) in a general setting. Our contribution is theoretical: we prove that a hard thresholding wavelet estimator attains a sharp rate of convergence under the mean integrated squared error (MISE) over Besov balls without imposing too restrictive assumptions on the model. Applications are given for two types of inverse problems: the deconvolution density estimation and the density estimation in a GARCH-type model, both improve existing results in this dependent context. Another application concerns the regression model with random design.
url http://dx.doi.org/10.1155/2014/403764
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