Abstract

DOS SANTOS SOUSA, ALEX RODRIGO. Asymmetric Prior in Wavelet Shrinkage. Rev.Colomb.Estad. [online]. 2022, vol.45, n.1, pp.41-63.  Epub Jan 18, 2023. ISSN 0120-1751.  https://doi.org/10.15446/rce.v45n1.92567.

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.

Keywords : asymmetric beta distribution; nonparametric regression; wavelet shrinkage.

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