Bayesian wavelet shrinkage with logistic prior

Abstract

Consider the nonparametric curve estimation problem. Wavelet shrinkage methods are applied to the data in the wavelet domain for noise reduction. After denoising, the function can be estimated by wavelet basis expansion. The present paper proposes a Bayesian approach for wavelet shrinkage with the use of a mixture of a point mass function at zero and the logistic distribution symmetric around zero as the prior distribution to the wavelet coefficients of an unknown function in models with additive Gaussian errors. Statistical properties such as bias, classical and Bayesian risks of the rules are analyzed and performances of the proposed rules are obtained in simulations studies involving the Donoho-Johnstone test functions. Application in a mass spectrometry real data set is done.