Wavelet estimation using Bayesian basis selection and basis averaging

Abstract

Wavelet shrinkage methods are widely recognized as a useful tool for non-parametric regression and signal recovery, while Bayesian approaches to choosing the shrinkage method in wavelet smoothing are known to be effective. In this paper we extend the Bayesian methodology to include choice among wavelet bases (and the Fourier basis), and averaging of the regression function estimates over different bases. This results in improved function estimates.