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Robust Wavelet Estimation to Eliminate Simultaneously the Effects of Boundary Problems, Outliers, and Correlated Noise
Joint Authors
Altaher, Alsaidi M.
Ismail, Mohd Tahir
Source
International Journal of Mathematics and Mathematical Sciences
Issue
Vol. 2012, Issue 2012 (31 Dec. 2012), pp.1-18, 18 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2012-11-27
Country of Publication
Egypt
No. of Pages
18
Main Subjects
Abstract EN
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.
American Psychological Association (APA)
Altaher, Alsaidi M.& Ismail, Mohd Tahir. 2012. Robust Wavelet Estimation to Eliminate Simultaneously the Effects of Boundary Problems, Outliers, and Correlated Noise. International Journal of Mathematics and Mathematical Sciences،Vol. 2012, no. 2012, pp.1-18.
https://search.emarefa.net/detail/BIM-511838
Modern Language Association (MLA)
Altaher, Alsaidi M.& Ismail, Mohd Tahir. Robust Wavelet Estimation to Eliminate Simultaneously the Effects of Boundary Problems, Outliers, and Correlated Noise. International Journal of Mathematics and Mathematical Sciences No. 2012 (2012), pp.1-18.
https://search.emarefa.net/detail/BIM-511838
American Medical Association (AMA)
Altaher, Alsaidi M.& Ismail, Mohd Tahir. Robust Wavelet Estimation to Eliminate Simultaneously the Effects of Boundary Problems, Outliers, and Correlated Noise. International Journal of Mathematics and Mathematical Sciences. 2012. Vol. 2012, no. 2012, pp.1-18.
https://search.emarefa.net/detail/BIM-511838
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-511838