Finite mixture modeling of censored and missing data using the\n multivariate skew-normal distribution

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