Abstract: We investigate the theoretical performance of Bayes factor estimators in wavelet regression models with independent and identically distributed errors that are not necessarily normally distributed. We compare these estimators in terms of their frequentist optimality in Besov spaces for a wide variety of error and prior distributions. Furthermore, we provide sufficient conditions that determine whether the underlying regression function belongs to a Besov space a-priori with probability one. We also study an adaptive estimator by considering an empirical Bayes estimation procedure of the Bayes factor estimator for a certain combination of error and prior distributions. Simulated examples are used to illustrate the performance of the empirical Bayes estimation procedure based on the proposed Bayes factor estimator, and compared with two recently proposed empirical Bayes estimators. An application to a dataset that was collected in an anaesthesiological study is also presented.
Key words and phrases: Bayesian inference, Besov spaces, empirical Bayes inference, nonparametric regression, optimality, wavelets.