Conditional mixture modelling for heavy-tailed and skewed data

Overparameterization is a serious concern for multivariate mixture models as it can lead to model overfitting and, as a result, mixture order underestimation. Parsimonious modelling is one of the most effective remedies in this context. In Gaussian mixture models, the majority of parameters is associated with covariance matrices and parsimonious models based on factor analysers and spectral decomposition of dispersion parameters are the most popular in literature. Some drawbacks of these models include the lack of flexibility in imposing different covariance structures for individual components and limitations in modelling compact clusters. Recently introduced conditional mixture models provide substantial flexibility in addressing these concerns. The components of such mixtures are formulated as a product of conditional distributions with univariate Gaussian densities being the primary choice. However, the presence of heavy tails or skewness in any dimension can lead to fitting problems. We propose a flexible model that is free of the above-mentioned limitations and name it a contaminated transformation conditional mixture model and demonstrate on a series of simulation studies that it can effectively account for skewness and heavy tails. Applications to real-life data sets show good results and highlight the promise of the proposed model.