  Finite mixture models have been widely used to model and analyze data from a
heterogeneous populations. Moreover, data of this kind can be missing or
subject to some upper and/or lower detection limits because of the restriction
of experimental apparatuses. Another complication arises when measures of each
population depart significantly from normality, for instance, asymmetric
behavior. For such data structures, we propose a robust model for censored
and/or missing data based on finite mixtures of multivariate skew-normal
distributions. This approach allows us to model data with great flexibility,
accommodating multimodality and skewness, simultaneously, depending on the
structure of the mixture components. We develop an analytically simple, yet
efficient, EM- type algorithm for conducting maximum likelihood estimation of
the parameters. The algorithm has closed-form expressions at the E-step that
rely on formulas for the mean and variance of the truncated multivariate
skew-normal distributions. Furthermore, a general information-based method for
approximating the asymptotic covariance matrix of the estimators is also
presented. Results obtained from the analysis of both simulated and real
datasets are reported to demonstrate the effectiveness of the proposed method.
The proposed algorithm and method are implemented in the new R package CensMFM.
