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Cross-validated wavelet block thresholding for non-Gaussian errors

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  • McGinnity, K.
  • Varbanov, R.
  • Chicken, E.

Abstract

Wavelet thresholding generally assumes independent, identically distributed normal errors when estimating functions in a nonparametric regression setting. VisuShrink and SureShrink are just two of the many common thresholding methods based on this assumption. When the errors are not normally distributed, however, few methods have been proposed. A distribution-free method for thresholding wavelet coefficients in nonparametric regression is described, which unlike some other non-normal error thresholding methods, does not assume the form of the non-normal distribution is known. Improvements are made to an existing even–odd cross-validation method by employing block thresholding and level dependence. The efficiency of the proposed method on a variety of non-normal errors, including comparisons to existing wavelet threshold estimators, is shown on simulated data.

Suggested Citation

  • McGinnity, K. & Varbanov, R. & Chicken, E., 2017. "Cross-validated wavelet block thresholding for non-Gaussian errors," Computational Statistics & Data Analysis, Elsevier, vol. 106(C), pages 127-137.
    • Handle: RePEc:eee:csdana:v:106:y:2017:i:c:p:127-137
    DOI: 10.1016/j.csda.2016.09.010
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    References listed on IDEAS

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    1. Fryzlewicz, Piotr, 2007. "Unbalanced Haar technique for nonparametric function estimation," LSE Research Online Documents on Economics 25216, London School of Economics and Political Science, LSE Library.
    2. Antoniadis, Anestis & Fryzlewicz, Piotr, 2006. "Parametric modelling of thresholds across scales in wavelet regression," LSE Research Online Documents on Economics 25832, London School of Economics and Political Science, LSE Library.
    3. Anestis Antoniadis & Piotr Fryzlewicz, 2006. "Parametric modelling of thresholds across scales in wavelet regression," Biometrika, Biometrika Trust, vol. 93(2), pages 465-471, June.
    4. Hee-Seok Oh & Douglas W. Nychka & Thomas C. M. Lee, 2007. "The Role of Pseudo Data for Robust Smoothing with Application to Wavelet Regression," Biometrika, Biometrika Trust, vol. 94(4), pages 893-904.
    5. Xue Wang & Andrew T. A. Wood, 2006. "Empirical Bayes block shrinkage of wavelet coefficients via the noncentral χ-super-2 distribution," Biometrika, Biometrika Trust, vol. 93(3), pages 705-722, September.
    6. Fryzlewicz, Piotr, 2007. "Unbalanced Haar Technique for Nonparametric Function Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 1318-1327, December.
    7. 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.
    8. Stuart Barber & Guy P. Nason, 2004. "Real nonparametric regression using complex wavelets," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(4), pages 927-939, November.
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