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On Optimality of Bayesian Wavelet Estimators

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  • Felix Abramovich
  • Umberto Amato
  • Claudia Angelini

Abstract

. We investigate the asymptotic optimality of several Bayesian wavelet estimators, namely, posterior mean, posterior median and Bayes Factor, where the prior imposed on wavelet coefficients is a mixture of a mass function at zero and a Gaussian density. We show that in terms of the mean squared error, for the properly chosen hyperparameters of the prior, all the three resulting Bayesian wavelet estimators achieve optimal minimax rates within any prescribed Besov space for p ≥ 2. For 1 ≤ p

Suggested Citation

  • 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.
    • Handle: RePEc:bla:scjsta:v:31:y:2004:i:2:p:217-234
    DOI: 10.1111/j.1467-9469.2004.02-087.x
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    Cited by:

    1. Felix Abramovich & Claudia Angelini & Daniela Canditiis, 2007. "Pointwise optimality of Bayesian wavelet estimators," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 59(3), pages 425-434, September.
    2. ter Braak, Cajo J.F., 2006. "Bayesian sigmoid shrinkage with improper variance priors and an application to wavelet denoising," Computational Statistics & Data Analysis, Elsevier, vol. 51(2), pages 1232-1242, November.
    3. Julyan Arbel & Ghislaine Gayraud & Judith Rousseau, 2013. "Bayesian Optimal Adaptive Estimation Using a Sieve Prior," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 40(3), pages 549-570, September.
    4. Julyan Arbel & Ghislaine Gayraud & Judith Rousseau, 2013. "Bayesian Optimal Adaptive Estimation Using a Sieve prior," Working Papers 2013-19, Center for Research in Economics and Statistics.
    5. 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.

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