On Optimality of Bayesian Wavelet Estimators

Felix Abramovich, Umberto Amato and Claudia Angelini

Scandinavian Journal of Statistics, 2004, vol. 31, issue 2, 217-234

Abstract: 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

Date: 2004
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Persistent link: https://EconPapers.repec.org/RePEc:bla:scjsta:v:31:y:2004:i:2:p:217-234

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