Robust Wavelet Estimation to Eliminate Simultaneously the Effects of Boundary Problems, Outliers, and Correlated Noise
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 r...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2012/963153 |
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| author | Alsaidi M. Altaher Mohd Tahir Ismail |
| author_facet | Alsaidi M. Altaher Mohd Tahir Ismail |
| author_sort | Alsaidi M. Altaher |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-8ced89a2232444a085df88ee3ec0edd6 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-8ced89a2232444a085df88ee3ec0edd62025-02-03T00:59:14ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252012-01-01201210.1155/2012/963153963153Robust Wavelet Estimation to Eliminate Simultaneously the Effects of Boundary Problems, Outliers, and Correlated NoiseAlsaidi M. Altaher0Mohd Tahir Ismail1School of Mathematical Sciences, Universiti Sains Malaysia, 11800 Penang, MalaysiaSchool of Mathematical Sciences, Universiti Sains Malaysia, 11800 Penang, MalaysiaClassical 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.http://dx.doi.org/10.1155/2012/963153 |
| spellingShingle | Alsaidi M. Altaher Mohd Tahir Ismail Robust Wavelet Estimation to Eliminate Simultaneously the Effects of Boundary Problems, Outliers, and Correlated Noise International Journal of Mathematics and Mathematical Sciences |
| title | Robust Wavelet Estimation to Eliminate Simultaneously the Effects of Boundary Problems, Outliers, and Correlated Noise |
| title_full | Robust Wavelet Estimation to Eliminate Simultaneously the Effects of Boundary Problems, Outliers, and Correlated Noise |
| title_fullStr | Robust Wavelet Estimation to Eliminate Simultaneously the Effects of Boundary Problems, Outliers, and Correlated Noise |
| title_full_unstemmed | Robust Wavelet Estimation to Eliminate Simultaneously the Effects of Boundary Problems, Outliers, and Correlated Noise |
| title_short | Robust Wavelet Estimation to Eliminate Simultaneously the Effects of Boundary Problems, Outliers, and Correlated Noise |
| title_sort | robust wavelet estimation to eliminate simultaneously the effects of boundary problems outliers and correlated noise |
| url | http://dx.doi.org/10.1155/2012/963153 |
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