A formulation for continuous mixtures of multivariate normal distributions

Shape mixtures of multivariate skew-normal distributions

Classes of shape mixtures of independent and dependent multivariate skew-normal distributions are considered and some of their main properties are studied. If interpreted from a Bayesian point of view, the results obtained in this paper bring tractability to the problem of inference for the shape parameter, that is, the posterior distribution can be written in analytic form. Robust inference fo...

Characteristic functions of scale mixtures of multivariate skew-normal distributions

Inference for multivariate normal mixtures

Multivariate normal mixtures provide a flexible model for high-dimensional data. They are widely used in statistical genetics, statistical finance, and other disciplines. Due to the unboundedness of the likelihood function, classical likelihoodbased methods, which may have nice practical properties, are inconsistent. In this paper, we recommend a penalized likelihood method for estimating the m...

Clustering Multivariate Normal Distributions

In this paper, we consider the task of clustering multivariate normal distributions with respect to the relative entropy into a prescribed number, k, of clusters using a generalization of Lloyd’s k-means algorithm [1]. We revisit this information-theoretic clustering problem under the auspices of mixed-type Bregman divergences, and show that the approach of Davis and Dhillon [2] (NIPS*06) can a...

Finite Mixtures of Multivariate Skew Laplace Distributions

In this paper, we propose finite mixtures of multivariate skew Laplace distributions to model both skewness and heavy-tailedness in the heterogeneous data sets. The maximum likelihood estimators for the parameters of interest are obtained by using the EM algorithm. We give a small simulation study and a real data example to illustrate the performance of the proposed mixture model.