Empirical Bayes block shrinkage of wavelet coefficients via the noncentral χ2 distribution

Empirical Bayes approaches to the shrinkage of empirical wavelet coefficients have generated considerable interest in recent years. Much of the work to date has focussed on shrinkage of individual wavelet coefficients in isolation. In this paper we propose an empirical Bayes approach to simultaneous shrinkage of wavelet coefficients in a block, based on the block sum of squares. Our approach exploits a useful identity satisfied by the noncentral chi(2) density and provides some tractable Bayesian block shrinkage procedures. Our numerical results indicate that the new procedures perform very well.