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Activity Number: 57 - Nonparametric Modeling I
Type: Contributed
Date/Time: Sunday, August 8, 2021 : 3:30 PM to 5:20 PM
Sponsor: Section on Nonparametric Statistics
Abstract #318056
Title: Asymmetric Prior in Wavelet Shrinkage
Author(s): Alex Rodrigo dos Santos Sousa*
Companies: University of São Paulo
Keywords: wavelets; nonparametric regression; beta prior distribution; bayesian statistics; shrinkage

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. In general, the asymmetric shrinkage rule outperformed classical symmetric rules both in simulation and real data application.

Authors who are presenting talks have a * after their name.

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