# A bayesian wavelet shrinkage rule under LINEX loss function

arXiv: https://arxiv.org/abs/2307.14279 · HTML: https://mlsanity.com/paper/2307.14279/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Jul 2023.

## Built on by (most cited first, 1 of 1)

- [Processing and classifying bird songs using wavelet techniques and supervised learning](https://mlsanity.com/paper/2609.10826/) (2026)

## Abstract (arXiv)

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.