On the fourth cumulant tensor in projection pursuit for a flexible class of skewed models

Projection pursuit is an exploratory data analysis approach for summarizing multivariate data through the search of interesting data projections. It relies on the maximization of an abnormality measure that quantifies the relevance of a projection to capture data non-normal features. The need to expand the estimation approaches to address projection pursuit has motivated its study within parametric frameworks. This is a follow-up work aimed at exploring the problem under a general class of distributions as it is the scale mixture of skew-normal family. Projection pursuit is examined by exploring the path going from the role played by the fourth cumulant tensor for addressing the problem to its connection with model parameters. The paper contributes to build a triangulation among linear algebra, projection pursuit and parametric statistics. A simulation study and an example with real data are also provided.