Abbreviated Journal Title
bayesian models; optimality; Sobolev and Besov spaces; nonparametric; regression; wavelet shrinkage; SELECTION; Statistics & Probability
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.
Annals of Statistics
Pensky, Marianna, "Frequentist optimality of Bayesian wavelet shrinkage rules for Gaussian and non-Gaussian noise" (2006). Faculty Bibliography 2000s. 7880.