Wavelet shrinkage based on the raised cosine prior

TL;DR

This paper introduces a Bayesian wavelet coefficient shrinkage method using a raised cosine prior, demonstrating superior performance over traditional methods in simulations and real data applications.

Contribution

It presents a novel Bayesian shrinkage rule with a raised cosine prior for wavelet coefficients, improving estimation accuracy in nonparametric regression.

Findings

Outperforms existing shrinkage methods in simulations

Reduces bias and variance in wavelet coefficient estimation

Effective in real data examples

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.