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Revista Colombiana de Estadística
Print version ISSN 0120-1751
Rev.Colomb.Estad. vol.45 no.1 Bogotá Jan./June 2022 Epub Jan 18, 2023
https://doi.org/10.15446/rce.v45n1.92567
Artículos originales de investigación
Asymmetric Prior in Wavelet Shrinkage
Priori asimétrico en contracción de ondículas
1 DEPARTMENT OF STATISTICS, INSTITUTE OF MATHEMATICS AND STATISTICS, UNIVERSITY OF SÃO PAULO, SÃO PAULO, BRAZIL
In bayesian wavelet shrinkage, the already proposed priors to wavelet coefficients are assumed to be symmetric around zero. Although this assumption is reasonable in many applications, it is not general. The present paper proposes the use of an asymmetric shrinkage rule based on the discrete mixture of a point mass function at zero and an asymmetric beta distribution as prior to the wavelet coefficients in a non-parametric regression model. Statistical properties such as bias, variance, classical and bayesian risks of the associated asymmetric rule are provided and performances of the proposed rule are obtained in simulation studies involving artificial asymmetric distributed coefficients and the Donoho-Johnstone test functions. Application in a seismic real dataset is also analyzed.
Key words: asymmetric beta distribution; nonparametric regression; wavelet shrinkage
En la contracción de las ondículas bayesianas, se supone que los coeficientes a priori ya propuestos de las ondículas son simétricos alrededor de cero. Aunque esta suposición es razonable en muchas aplicaciones, no es general. El presente artículo propone el uso de una regla de contracción asimétrica basada en la mezcla discreta de una función de masa puntual en cero y una distribución beta asimétrica como priori de los coeficientes de ondícula en un modelo de regresión no paramétrico. Se proporcionan propiedades estadísticas tales como sesgo, varianza, riesgos clásicos y bayesianos de la regla asimétrica asociada y se obtienen los rendimientos de la regla propuesta en estudios de simulación que involucran coeficientes distribuidos asimétricos artificiales y las funciones de prueba de Donoho-Johnstone. También se analiza la aplicación en un conjunto de datos sísmicos reales.
Palabras clave: contracción de las ondículas; distribución beta asimétrica; regresión no paramétrico
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Received: December 2020; Accepted: August 2021
This is an open-access article distributed under the terms of the Creative Commons Attribution License
