GENERALIZED WAVELET THRESHOLDING: ESTIMATION AND HYPOTHESIS TESTING WITH APPLICATIONS TO ARRAY COMPARATIVE

Wavelets have gained considerable popularity within the statistical arena in the context of nonparametric regression. When modeling data of the form y = f + , the objective is to estimate the unknown ‘true ’ function f with small risk, based on sampled data y contaminated with random (usually Gaussian) noise . Wavelet shrinkage and thresholding techniques have proved to be quite effective in recovering the true function f, particularly when f is spatially inhomogeneous. Recently, Johnstone and Silverman (2005b) proposed using empirical Bayes methods for level-dependent threshold selection in wavelet shrinkage. Using the posterior median estimator, their approach amounts to a random thresholding procedure with impressive mean squared error (MSE) results. At each level, their approach considers a two-component mixture prior for each of the wavelet coef-ficients independently. This mixture prior inherently assumes that the wavelet coefficients are symmetrically distributed about zero. Depending on the choice of wavelet filter and the interesting attributes of th