Semiparametric Gaussian Variance-Mean Mixtures for Heavy-Tailed and Skewed Data

Abstract

There is a need for new classes of flexible multivariate distributions that can capture heavy tails and skewness without being so flexible as to fully incur the curse of dimensionality intrinsic to nonparametric density estimation. We focus on the family of Gaussian variance-mean mixtures, which have received limited attention in multivariate settings beyond simple special cases. By using a Bayesian semiparametric approach, we allow the data to infer about the unknown mixing distribution. Properties are considered and an approach to posterior computation is developed relying on Markov chain Monte Carlo. The methods are evaluated through simulation studies and applied to a variety of applications, illustrating their flexible performance in characterizing heavy tails, tail dependence, and skewness.