Robust model-based clustering via mixtures of skew-t distributions with missing information

Abstract

Multivariate mixture modeling approach using the skew-t distribution has emerged as a powerful and flexible tool for robust model-based clustering. The occurrence of missing data is a ubiquitous problem in almost every scientific field. In this paper, we offer a computationally flexible EM-type procedure for learning multivariate skew-t mixture models to deal with missing data under missing at random mechanisms. Further, we present an information-based approach to approximating the asymptotic covariance matrix of the maximum likelihood estimators using the outer product of the scores. To assist the development and ease the implementation of our algorithm, two auxiliary permutation matrices are utilized for fast determination of the observed and missing parts of each observation. The practical usefulness of the proposed methodology is illustrated through simulations with varying proportions of artificial missing values and a real data example with genuine missing values.