Bayesian wavelet shrinkage for low SNR data based on the Epanechnikov kernel

TL;DR

This paper introduces a Bayesian wavelet shrinkage method using an Epanechnikov kernel prior, specifically designed for low SNR data, and demonstrates its superior performance over existing methods through simulations and real EEG data application.

Contribution

It proposes a novel Bayesian shrinkage rule with an Epanechnikov kernel prior for wavelet coefficients, optimized for low SNR scenarios.

Findings

Outperforms standard and Bayesian methods in simulations

Provides explicit formula and statistical properties of the shrinkage rule

Successfully applied to real EEG data

Abstract

Consider the univariate nonparametric regression model with additive Gaussian noise and the representation of the unknown regression function in terms of a wavelet basis. We propose a shrinkage rule to estimate the wavelet coefficients obtained by mixing a point mass function at zero with the Epanechnikov distribution as a prior for the coefficients. The proposed rule proved to be suitable for application in scenarios with low signal-to-noise ratio datasets and outperformed standard and Bayesian methods in simulation studies. Statistical properties, such as squared bias and variance, are provided, and an explicit expression of the rule is obtained. An application of the rule is demonstrated using a real EEG dataset.