Asymptotic form of the Kullback–Leibler divergence for multivariate asymmetric heavy-tailed distributions

Abstract

An asymptotic expression for the Kullback–Leibler (KL) divergence measure of multivariate skew-t distributions (MST) is derived. This novel class of flexible family distributions incorporates a shape and degree of freedom parameters, in order to manipulate the skewness and heavy-tail presence of the data, respectively. The quadratic form expressions of MST models are used to provide asymptotic measures. Additional inequalities for MST entropy and simulation studies are reported. Finally, the expected values of the KL divergence of a sample correlation matrix obtained by Pearson’s correlation coefficient are discussed.