The Annals of Statistics
- Ann. Statist.
- Volume 34, Number 2 (2006), 769-807.
Frequentist optimality of Bayesian wavelet shrinkage rules for Gaussian and non-Gaussian noise
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 rate and explain why it happens.
Ann. Statist., Volume 34, Number 2 (2006), 769-807.
First available in Project Euclid: 27 June 2006
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 62G08: Nonparametric regression
Secondary: 62C10: Bayesian problems; characterization of Bayes procedures
Pensky, Marianna. Frequentist optimality of Bayesian wavelet shrinkage rules for Gaussian and non-Gaussian noise. Ann. Statist. 34 (2006), no. 2, 769--807. doi:10.1214/009053606000000128. https://projecteuclid.org/euclid.aos/1151418240