On optimality of Bayesian wavelet estimators

Felix Abramovich*, Umberto Amato, Claudia Angelini

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

23 Scopus citations


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 Bp,qs for p ≥ 2. For 1 ≤ p < 2, the Bayes Factor is still optimal for (2s + 2)/(2s+1) ≤ p < 2 and always outperforms the posterior mean and the posterior median that can achieve only the best possible rates for linear estimators in this case.

Original languageEnglish
Pages (from-to)217-234
Number of pages18
JournalScandinavian Journal of Statistics
Issue number2
StatePublished - Jun 2004


  • Bayes Factor
  • Bayes model
  • Besov spaces
  • Minimax estimation
  • Non-linear estimation
  • Non-parametric regression
  • Posterior mean
  • Posterior median
  • Wavelets


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