A Bayesian wavelet shrinkage rule under LINEX loss function

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 the 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.

Keywords

• Wavelet shrinkage
• LINEX loss
• nonparametric regression
• Bayesian inference
• logistic distribution