Analytic calculations for the EM algorithm for multivariate skew-tt mixture models

The em algorithm can be used to compute maximum likelihood estimates of model parameters for skew-tt mixture models. We show that the intractable expectations needed in the e-step can be written out analytically. These closed form expressions bypass the need for numerical estimation procedures, such as Monte Carlo methods, leading to accurate calculation of maximum likelihood estimates. Our approach is illustrated on two real data sets.