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Flexible empirical Bayes estimation for wavelets

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  • Merlise Clyde
  • Edward I. George

Abstract

Wavelet shrinkage estimation is an increasingly popular method for signal denoising and compression. Although Bayes estimators can provide excellent mean‐squared error (MSE) properties, the selection of an effective prior is a difficult task. To address this problem, we propose empirical Bayes (EB) prior selection methods for various error distributions including the normal and the heavier‐tailed Student t‐distributions. Under such EB prior distributions, we obtain threshold shrinkage estimators based on model selection, and multiple‐shrinkage estimators based on model averaging. These EB estimators are seen to be computationally competitive with standard classical thresholding methods, and to be robust to outliers in both the data and wavelet domains. Simulated and real examples are used to illustrate the flexibility and improved MSE performance of these methods in a wide variety of settings.

Suggested Citation

  • Merlise Clyde & Edward I. George, 2000. "Flexible empirical Bayes estimation for wavelets," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(4), pages 681-698.
  • Handle: RePEc:bla:jorssb:v:62:y:2000:i:4:p:681-698
    DOI: 10.1111/1467-9868.00257
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    File URL: https://doi.org/10.1111/1467-9868.00257
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    Citations

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    Cited by:

    1. P. J. Brown & M. Vannucci & T. Fearn, 2002. "Bayes model averaging with selection of regressors," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(3), pages 519-536, August.
    2. repec:dau:papers:123456789/13437 is not listed on IDEAS
    3. Peter Müeller & Fernando A. Quintana & Garritt Page, 2018. "Nonparametric Bayesian inference in applications," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 27(2), pages 175-206, June.
    4. Andrew Gelman, 2003. "A Bayesian Formulation of Exploratory Data Analysis and Goodness‐of‐fit Testing," International Statistical Review, International Statistical Institute, vol. 71(2), pages 369-382, August.
    5. Reményi, Norbert & Vidakovic, Brani, 2013. "Λ-neighborhood wavelet shrinkage," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 404-416.
    6. Gabriel Huerta, 2005. "Multivariate Bayes Wavelet shrinkage and applications," Journal of Applied Statistics, Taylor & Francis Journals, vol. 32(5), pages 529-542.
    7. 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.
    8. Joyee Ghosh & Amy H. Herring & Anna Maria Siega-Riz, 2011. "Bayesian Variable Selection for Latent Class Models," Biometrics, The International Biometric Society, vol. 67(3), pages 917-925, September.
    9. Stuart Barber & Guy P. Nason & Bernard W. Silverman, 2002. "Posterior probability intervals for wavelet thresholding," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(2), pages 189-205, May.
    10. Meiri, Ronen & Zahavi, Jacob, 2006. "Using simulated annealing to optimize the feature selection problem in marketing applications," European Journal of Operational Research, Elsevier, vol. 171(3), pages 842-858, June.
    11. Enrique Moral-Benito, 2015. "Model Averaging In Economics: An Overview," Journal of Economic Surveys, Wiley Blackwell, vol. 29(1), pages 46-75, February.
    12. 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.
    13. 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.
    14. Wang, Y. & Daniels, M.J., 2013. "Bayesian modeling of the dependence in longitudinal data via partial autocorrelations and marginal variances," Journal of Multivariate Analysis, Elsevier, vol. 116(C), pages 130-140.
    15. Sonia Petrone & Stefano Rizzelli & Judith Rousseau & Catia Scricciolo, 2014. "Empirical Bayes methods in classical and Bayesian inference," METRON, Springer;Sapienza Università di Roma, vol. 72(2), pages 201-215, August.

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