Maximum likelihood inference for the multivariate tt mixture model

Multivariate tt mixture (TMIX) models have emerged as a powerful tool for robust modeling and clustering of heterogeneous continuous multivariate data with observations containing longer than normal tails or atypical observations. In this paper, we explicitly derive the score vector and Hessian matrix of TMIX models to approximate the information matrix under the general and three special cases. As a result, the standard errors of maximum likelihood (ML) estimators are calculated using the outer-score, Hessian matrix, and sandwich-type methods. We have also established some asymptotic properties under certain regularity conditions. The utility of the new theory is illustrated with the analysis of real and simulated data sets.