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A penalised data-driven block shrinkage approach to empirical Bayes wavelet estimation

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  • Wang, Xue
  • Walker, Stephen G.

Abstract

In this paper we propose a simple Bayesian block wavelet shrinkage method for estimating an unknown function in the presence of Gaussian noise. A data-driven procedure which can adaptively choose the block size and the shrinkage level at each resolution level is provided. The asymptotic property of the proposed method, BBN (Bayesian BlockNorm shrinkage), is investigated in the Besov sequence space. The numerical performance and comparisons with some of existing wavelet denoising methods show that the new method can achieve good performance but with the least computational time.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:80:y:2010:i:11-12:p:990-996
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    References listed on IDEAS

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    1. Abramovich, Felix & Besbeas, Panagiotis & Sapatinas, Theofanis, 2002. "Empirical Bayes approach to block wavelet function estimation," Computational Statistics & Data Analysis, Elsevier, vol. 39(4), pages 435-451, June.
    2. 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.
    3. Felix Abramovich & Umberto Amato & Claudia Angelini, 2004. "On Optimality of Bayesian Wavelet Estimators," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 31(2), pages 217-234, June.
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