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- Title
On Optimality of Bayesian Wavelet Estimators.
- Authors
Abramovich, Felix; Amato, Umberto; Angelini, Claudia
- 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 < 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.
- Subjects
BAYESIAN analysis; WAVELETS (Mathematics); CHEBYSHEV approximation; BESOV spaces; NONLINEAR wave equations; NONPARAMETRIC statistics; REGRESSION analysis; MATHEMATICAL statistics
- Publication
Scandinavian Journal of Statistics, 2004, Vol 31, Issue 2, p217
- ISSN
0303-6898
- Publication type
Article
- DOI
10.1111/j.1467-9469.2004.02-087.x