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Frequentist optimality of Bayesian wavelet shrinkage rules for Gaussian and non-Gaussian noise. (English) Zbl 1095.62049

Summary: The present paper investigates theoretical performance of various Bayesian wavelet shrinkage rules in a nonparametric regression model with i.i.d. errors which are not necessarily normally distributed. The main purpose is comparison of various Bayesian models in terms of their frequentist asymptotic optimality in Sobolev and Besov spaces.
We establish a relationship between hyperparameters, verify that the majority of Bayesian models studied so far achieve theoretical optimality, state which Bayesian models cannot achieve optimal convergence rates and explain why it happens.

MSC:

62G08 Nonparametric regression and quantile regression
62C10 Bayesian problems; characterization of Bayes procedures
42C40 Nontrigonometric harmonic analysis involving wavelets and other special systems
62F15 Bayesian inference

Software:

EBayesThresh
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References:

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