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On Optimality of Bayesian Wavelet Estimators
Author(s) -
Abramovich Felix,
Amato Umberto,
Angelini Claudia
Publication year - 2004
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/j.1467-9469.2004.02-087.x
Subject(s) - mathematics , estimator , hyperparameter , minimax , wavelet , bayesian probability , prior probability , statistics , bayes estimator , bayes' theorem , gaussian , mean squared error , algorithm , mathematical optimization , artificial intelligence , computer science , physics , quantum mechanics
. 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 < 2, the Bayes Factor is still optimal for (2 s +2)/(2 s +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.