  The present paper proposes a bayesian approach for wavelet shrinkage with the
use of a shrinkage prior based on the generalized secant hyperbolic
distribution symmetric around zero in a nonparemetric regression problem. This
shrinkage prior allows the control of the kurtosis of the coefficients, which
impacts on the level of shrinkage on its extreme values. Statistical properties
such as bias, variance, classical and bayesian risks of the rule are analyzed
and performances of the proposed rule are obtained in simulations studies
involving the Donoho-Johnstone test functions. Application of the proposed
shrinker in denoising Brazilian stock market dataset is also provided.
