A class of priors to perform asymmetric Bayesian wavelet shrinkage

Abstract

This paper proposes a class of asymmetric priors to perform Bayesian wavelet shrinkage in the standard nonparametric regression model with Gaussian error. The priors are composed by mixtures of a point mass function at zero and one of the following distributions: asymmetric beta, Kumaraswamy, asymmetric triangular or skew normal. Statistical properties of the associated shrinkage rules such as squared bias, variance and risks are obtained numerically and discussed. Monte Carlo simulation studies are described to evaluate the performances of the rules against standard techniques. An application of the asymmetric rules to a stock market index time series is also illustrated.