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Empirical Bayes block shrinkage of wavelet coefficients via the noncentral χ-super-2 distribution

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  • Xue Wang
  • Andrew T. A. Wood

Abstract

Empirical Bayes approaches to the shrinkage of empirical wavelet coefficients have generated considerable interest in recent years. Much of the work to date has focussed on shrinkage of individual wavelet coefficients in isolation. In this paper we propose an empirical Bayes approach to simultaneous shrinkage of wavelet coefficients in a block, based on the block sum of squares. Our approach exploits a useful identity satisfied by the noncentral χ-super-2 density and provides some tractable Bayesian block shrinkage procedures. Our numerical results indicate that the new procedures perform very well. Copyright 2006, Oxford University Press.

Suggested Citation

  • 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.
    • Handle: RePEc:oup:biomet:v:93:y:2006:i:3:p:705-722
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    File URL: http://hdl.handle.net/10.1093/biomet/93.3.705
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    Cited by:

    1. Reményi, Norbert & Vidakovic, Brani, 2013. "Λ-neighborhood wavelet shrinkage," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 404-416.
    2. Nilotpal Sanyal & Marco A. R. Ferreira, 2017. "Bayesian Wavelet Analysis Using Nonlocal Priors with an Application to fMRI Analysis," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 79(2), pages 361-388, November.
    3. Wang, Xue & Walker, Stephen G., 2010. "A penalised data-driven block shrinkage approach to empirical Bayes wavelet estimation," Statistics & Probability Letters, Elsevier, vol. 80(11-12), pages 990-996, June.
    4. 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.

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