  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.
