Asymmetric prior in wavelet shrinkage

TL;DR

This paper introduces an asymmetric prior for wavelet coefficients in Bayesian wavelet shrinkage, allowing for better modeling of asymmetric coefficient distributions in non-parametric regression, with demonstrated improvements in simulations and real data.

Contribution

It proposes a novel asymmetric shrinkage rule using a mixture of a point mass and an asymmetric beta distribution, extending prior models.

Findings

The asymmetric rule improves estimation accuracy in asymmetric coefficient scenarios.

Simulation results show better bias and risk properties compared to symmetric priors.

Application to seismic data demonstrates practical effectiveness.

Abstract

In bayesian wavelet shrinkage, the already proposed priors to wavelet coefficients are assumed to be symmetric around zero. Although this assumption is reasonable in many applications, it is not general. The present paper proposes the use of an asymmetric shrinkage rule based on the discrete mixture of a point mass function at zero and an asymmetric beta distribution as prior to the wavelet coefficients in a non-parametric regression model. Statistical properties such as bias, variance, classical and bayesian risks of the associated asymmetric rule are provided and performances of the proposed rule are obtained in simulation studies involving artificial asymmetric distributed coefficients and the Donoho-Johnstone test functions. Application in a seismic real dataset is also analyzed.