A bayesian wavelet shrinkage rule under LINEX loss function

TL;DR

This paper introduces a Bayesian wavelet shrinkage rule optimized for asymmetric LINEX loss, improving feature detection in nonparametric regression with Gaussian errors, validated through simulations and real data application.

Contribution

It proposes a novel wavelet shrinkage rule using LINEX loss and a mixture prior, addressing asymmetry in over- and underestimation risks.

Findings

The rule effectively detects features like peaks and discontinuities.

Simulation results show improved performance over standard methods.

Application to infrared spectra demonstrates practical utility.

Abstract

This work proposes a wavelet shrinkage rule under asymmetric LINEX loss function and a mixture of a point mass function at zero and the logistic distribution as prior distribution to the wavelet coefficients in a nonparametric regression model with gaussian error. Underestimation of a significant wavelet coefficient can lead to a bad detection of features of the unknown function such as peaks, discontinuities and oscillations. It can also occur under asymmetrically distributed wavelet coefficients. Thus the proposed rule is suitable when overestimation and underestimation have asymmetric losses. Statistical properties of the rule such as squared bias, variance, frequentist and bayesian risks are obtained. Simulation studies are conducted to evaluate the performance of the rule against standard methods and an application in a real dataset involving infrared spectra is provided.