Empirical Bayes estimation in wavelet nonparametric regression

ABSTRACT Bayesian methods based on hierarchical mixture models have demonstrated excellent mean squared error properties in constructing data dependent shrinkage estimators in wavelets, however, subjective elicitation of the hyperparameters is challenging. In this chapter we use an Empirical Bayes approach to estimate the hyperparameters for each level of the wavelet decomposition, bypassing the usual difficulty of hyperparameter specification in the hierarchical model. The EB approach is computationally competitive with standard methods and offers improved MSE performance over several Bayes and classical estimators in a wide variety of examples. 1 Introduction Wavelet shrinkage has become an increasingly popular method for compression and denoising of data in the context of signal and image processing as well as nonparametric regression (Donoho and Johnstone (1994, 1995). The nonparametric regression model can be specified as Yi = fi + ffli where fi represents the underlying unknown mean function and ffli are independent N (0; oe2) random errors, representing additive white noise. In the wavelet domain, this can be equivalently expressed a