Statistica Sinica 10(2000), 109-128

WAVELET ESTIMATION USING BAYESIAN BASIS

SELECTION AND BASIS AVERAGING

Robert Kohn, J. S. Marron$^*$ and Paul Yau$^*$

University of New South Wales and $^*$University of North Carolina, Chapel Hill

Abstract: Wavelet shrinkage methods are widely recognized as a useful tool for nonparametric 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.

Key words and phrases: Empirical Bayes, Fourier series, nonparametric regression.