Robust wavelet estimation to eliminate simultaneously the effects of boundary problems, outliers, and correlated noise
type: Item
instance of: scholarly article
title: Robust wavelet estimation to eliminate simultaneously the effects of boundary problems, outliers, and correlated noise
zbMATH Open document ID: 1253.94019
DOI: 10.1155/2012/963153
author: Alsaidi M. Altaher
author: Mohd. Tahir Ismail
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 2012-12-18T00:00:00Z
review text: Summary: Classical wavelet thresholding methods suffer from boundary problems caused by the application of the wavelet transformations to a finite signal. As a result, large bias at the edges and artificial wiggles occur when the classical boundary assumptions are not satisfied. Although polynomial wavelet regression and local polynomial wavelet regression effectively reduce the risk of this problem, the estimates from these two methods can be easily affected by the presence of correlated noise and outliers, giving inaccurate estimates. This paper introduces two robust methods in which the effects of boundary problems, outliers, and correlated noise are simultaneously taken into account. The proposed methods combine thresholding estimator with either a local polynomial model or a polynomial model using the generalized least squares method instead of the ordinary one. A primary step that involves removing the outlying observations through a statistical function is considered as well. The practical performance of the proposed methods has been evaluated through simulation experiments and real data examples. The results are strong evidence that the proposed method is extremely effective in terms of correcting the boundary bias and eliminating the effects of outliers and correlated noise.
Mathematics Subject Classification ID: 94A11
Mathematics Subject Classification ID: 42C40
Mathematics Subject Classification ID: 62M10
Mathematics Subject Classification ID: 94A12
zbMATH DE Number: 6116558
zbMATH Keywords: wavelet thresholding methods
zbMATH Keywords: robust methods
describes a project that uses: EBayesThresh
describes a project that uses: astsa
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2012/963153
OpenAlex ID: W2139323286
Wikidata QID: Q58705285
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description: scientific article; zbMATH DE number 6116558