Multivariate skew t-distribution: Asymptotics for parameter estimators and extension to skew t-copula

Abstract

Symmetric elliptical distributions have been intensively used in data modeling and ro-bustness studies. The area of applications was considerably widened after transforming elliptical distributions into the skew elliptical ones that preserve several good properties of the corresponding symmetric distributions and increase possibilities of data modeling. We consider three-parameter p-variate skew t-distribution where p-vector µ is the location parameter, Σ: p × p is the positive definite scale parameter, p-vector α is the skewness or shape parameter, and the number of degrees of freedom ν is fixed. Special attention is paid to the two-parameter distribution when µ = 0 that is useful for construction of the skew t-copula. Expressions of the parameters are presented through the moments and parameter estimates are found by the method of moments. Asymptotic normality is established for the estimators of Σ and α. Convergence to the asymptotic distributions is examined in simulation experiments.