Kurtosis control in wavelet shrinkage with generalized secant hyperbolic prior

TL;DR

This paper introduces a Bayesian wavelet shrinkage method using a generalized secant hyperbolic prior that controls kurtosis, improving denoising performance in regression and real-world financial data.

Contribution

It proposes a novel prior for wavelet coefficients that allows explicit kurtosis control, enhancing shrinkage adaptivity in Bayesian wavelet denoising.

Findings

The method effectively controls kurtosis of coefficients.

Simulation results show improved denoising performance.

Application to stock data demonstrates practical utility.

Abstract

The present paper proposes a bayesian approach for wavelet shrinkage with the use of a shrinkage prior based on the generalized secant hyperbolic distribution symmetric around zero in a nonparemetric regression problem. This shrinkage prior allows the control of the kurtosis of the coefficients, which impacts on the level of shrinkage on its extreme values. Statistical properties such as bias, variance, classical and bayesian risks of the rule are analyzed and performances of the proposed rule are obtained in simulations studies involving the Donoho-Johnstone test functions. Application of the proposed shrinker in denoising Brazilian stock market dataset is also provided.