Wavelet shrinkage based on the raised cosine prior

Abstract

We propose a Bayesian shrinkage rule to estimate the wavelet coefficients in a nonparametric regression model with Gaussian errors, based on a mixture of a point mass function at zero and a symmetric, zero-centered raised cosine distribution prior. The proposed rule outperformed established shrinkage and thresholding methods in specific scenarios of signal-to-noise ratio and sample size values in conducted simulation studies involving the so-called Donoho and Johnstone test functions. Statistical properties of the rule, such as squared bias, variance, and risks, are analyzed, and two illustrations in real datasets are provided.