Pointwise optimality of Bayesian wavelet estimators

Felix Abramovich*, Claudia Angelini, Daniela De Canditiis

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

We consider pointwise mean squared errors of several known Bayesian wavelet estimators, namely, posterior mean, posterior median and Bayes Factor, where the prior imposed on wavelet coefficients is a mixture of an atom of probability zero and a Gaussian density. We show that for the properly chosen hyperparameters of the prior, all the three estimators are (up to a log-factor) asymptotically minimax within any prescribed Besov ball Bp s, q (M). We discuss the Bayesian paradox and compare the results for the pointwise squared risk with those for the global mean squared error.

Original languageEnglish
Pages (from-to)425-434
Number of pages10
JournalAnnals of the Institute of Statistical Mathematics
Volume59
Issue number3
DOIs
StatePublished - Sep 2007

Keywords

  • Bayes factor
  • Bayes model
  • Bayesian paradox
  • Besov spaces
  • Minimax rates
  • Nonparametric regression
  • Point estimation
  • Posterior mean
  • Posterior median
  • Wavelets

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