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 \(B^{s}_{p},_{q} (M)\). We discuss the Bayesian paradox and compare the results for the pointwise squared risk with those for the global mean squared error.
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Abramovich, F., Angelini, C. & De Canditiis, D. Pointwise optimality of Bayesian wavelet estimators. AISM 59, 425–434 (2007). https://doi.org/10.1007/s10463-006-0071-7
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DOI: https://doi.org/10.1007/s10463-006-0071-7