Skewness-Based Projection Pursuit as an Eigenvector Problem in Scale Mixtures of Skew-Normal Distributions

This paper addresses the projection pursuit problem assuming that the distribution of the input vector belongs to the flexible and wide family of multivariate scale mixtures of skew normal distributions. Under this assumption, skewness-based projection pursuit is set out as an eigenvector problem, described in terms of the third order cumulant matrix, as well as an eigenvector problem that involves the simultaneous diagonalization of the scatter matrices of the model. Both approaches lead to dominant eigenvectors proportional to the shape parametric vector, which accounts for the multivariate asymmetry of the model; they also shed light on the parametric interpretability of the invariant coordinate selection method and point out some alternatives for estimating the projection pursuit direction. The theoretical findings are further investigated through a simulation study whose results provide insights about the usefulness of skewness model-based projection pursuit in the statistical practice.

Analysis of antibody data using Finite Mixture Models based on Scale Mixtures of Skew-Normal distributions

Finite mixture models have been widely used in antibody (or serological) data analysis in order to help classifying individuals into either antibody-positive or antibody-negative. The most popular models are the so-called Gaussian mixture models which assume a Normal distribution for each component of a mixture. In this work, we propose the use of finite mixture models based on a flexible class of scale mixtures of Skew-Normal distributions for serological data analysis. These distributions are sufficiently flexible to describe right and left asymmetry often observed in the distributions associated with hypothetical antibody-negative and antibody-positive individuals, respectively. We illustrate the advantage of these alternative mixture models with a data set of 406 individuals in which antibodies against six different human herpesviruses were measured in the context of Myalgic Encephalomyelitis/Chronic Fatigue Syndrome.