Finite mixture modeling of censored data using the multivariate Student-t distribution

Finite mixture models have been widely used for the modelling and analysis of data froma heterogeneous population. Moreover, these kind of data can be subjected to some upper and/or lower detection limits because of the restriction of experimental apparatus. Another complication arises when measures of each population depart significantly from normality, for instance, in the presence of heavy tails or atypical observations. For such data structures, we propose a robust model for censored data based on finite mixtures of multivariate Student-t distributions. This approach allows us to model data with great flexibility, accommodating multimodality, heavy tails and also skewness 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 multivariate truncated Student-t distributions. Further, 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 data sets are reported to demonstrate the effectiveness of the proposed methodology. The proposed algorithm and methods are implemented in the new R package CensMixReg.