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 coe±cients 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. We discuss the Bayesian paradox and compare the results for the pointwise squared risk with those for the global mean squared error
Anno
2007
Autori IAC
Tipo pubblicazione
Altri Autori
Abramovich F.; Angelini C.; De Canditiis D.
Editore
Springer
Rivista
Annals of the Institute of Statistical Mathematics