A class of priors to perform asymmetric Bayesian wavelet shrinkage

TL;DR

This paper introduces a new class of asymmetric priors for Bayesian wavelet shrinkage, enhancing nonparametric regression by improving shrinkage rules with various asymmetric distributions, evaluated through simulations and real data.

Contribution

It proposes novel asymmetric priors combining point mass and various distributions for Bayesian wavelet shrinkage, with detailed statistical analysis and practical evaluation.

Findings

Shrinkage rules show improved bias and variance properties.

Simulation results outperform standard techniques.

Application to stock data demonstrates practical utility.

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.