  Finite mixtures of skew distributions provide a flexible tool for modelling
heterogeneous data with asymmetric distributional features. However, parameter
estimation via the Expectation-Maximization (EM) algorithm can become very
time-consuming due to the complicated expressions involved in the E-step that
are numerically expensive to evaluate. A more time-efficient implementation of
the EM algorithm was recently proposed which allows each component of the
mixture model to be evaluated in parallel. In this paper, we develop a block
implementation of the EM algorithm that facilitates the calculations in the E-
and M-steps to be spread across a larger number of threads. We focus on the
fitting of finite mixtures of multivariate skew normal and skew
t-distributions, and show that both the E- and M-steps in the EM algorithm can
be modified to allow the data to be split into blocks. The approach can be
easily implemented for use by multicore and multi-processor machines. It can
also be applied concurrently with the recently proposed multithreaded EM
algorithm to achieve further reduction in computation time. The improvement in
time performance is illustrated on some real datasets.
