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Robust Wavelet Estimation to Eliminate Simultaneously the Effects of Boundary Problems, Outliers, and Correlated Noise

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  • Alsaidi M. Altaher
  • Mohd Tahir Ismail

Abstract

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.

Suggested Citation

  • Alsaidi M. Altaher & Mohd Tahir Ismail, 2012. "Robust Wavelet Estimation to Eliminate Simultaneously the Effects of Boundary Problems, Outliers, and Correlated Noise," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2012, pages 1-18, November.
    • Handle: RePEc:hin:jijmms:963153
    DOI: 10.1155/2012/963153
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    2. Oh, Hee-Seok & Lee, Thomas C. M., 2005. "Hybrid local polynomial wavelet shrinkage: wavelet regression with automatic boundary adjustment," Computational Statistics & Data Analysis, Elsevier, vol. 48(4), pages 809-819, April.
    3. Sarah Gelper & Roland Fried & Christophe Croux, 2010. "Robust forecasting with exponential and Holt-Winters smoothing," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 29(3), pages 285-300.
    4. Iain M. Johnstone & Bernard W. Silverman, 1997. "Wavelet Threshold Estimators for Data with Correlated Noise," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 59(2), pages 319-351.
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