A Bayesian wavelet shrinkage rule under LINEX loss function

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 wa...

Full description

Saved in:
Bibliographic Details
Main Author: Alex Rodrigo dos Santos Sousa
Format: Article
Language:English
Published: Taylor & Francis 2024-12-01
Series:Research in Statistics
Subjects:
Online Access:https://www.tandfonline.com/doi/10.1080/27684520.2024.2362926
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1846143258131955712
author Alex Rodrigo dos Santos Sousa
author_facet Alex Rodrigo dos Santos Sousa
author_sort Alex Rodrigo dos Santos Sousa
collection DOAJ
description 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.
format Article
id doaj-art-1c76624a9b0545d4804c6d66b6c95333
institution Kabale University
issn 2768-4520
language English
publishDate 2024-12-01
publisher Taylor & Francis
record_format Article
series Research in Statistics
spelling doaj-art-1c76624a9b0545d4804c6d66b6c953332024-12-02T19:00:47ZengTaylor & FrancisResearch in Statistics2768-45202024-12-012110.1080/27684520.2024.2362926A Bayesian wavelet shrinkage rule under LINEX loss functionAlex Rodrigo dos Santos Sousa0Department of Statistics, Universidade Estadual de Campinas, Campinas, BrazilThis 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.https://www.tandfonline.com/doi/10.1080/27684520.2024.2362926Wavelet shrinkageLINEX lossnonparametric regressionBayesian inferencelogistic distribution
spellingShingle Alex Rodrigo dos Santos Sousa
A Bayesian wavelet shrinkage rule under LINEX loss function
Research in Statistics
Wavelet shrinkage
LINEX loss
nonparametric regression
Bayesian inference
logistic distribution
title A Bayesian wavelet shrinkage rule under LINEX loss function
title_full A Bayesian wavelet shrinkage rule under LINEX loss function
title_fullStr A Bayesian wavelet shrinkage rule under LINEX loss function
title_full_unstemmed A Bayesian wavelet shrinkage rule under LINEX loss function
title_short A Bayesian wavelet shrinkage rule under LINEX loss function
title_sort bayesian wavelet shrinkage rule under linex loss function
topic Wavelet shrinkage
LINEX loss
nonparametric regression
Bayesian inference
logistic distribution
url https://www.tandfonline.com/doi/10.1080/27684520.2024.2362926
work_keys_str_mv AT alexrodrigodossantossousa abayesianwaveletshrinkageruleunderlinexlossfunction
AT alexrodrigodossantossousa bayesianwaveletshrinkageruleunderlinexlossfunction