Projection Pursuit mediante un enfoque paramétrico basado en distribuciones multivariantes con asimetría y kurtosis
Projection pursuit (PP) is an exploratory data analysis technique aimed at finding low dimensional representations of data that reveal some kind of insightful structure. To assess the interestingness of a projection, several indices quantifying the non-normal features of multivariate data have been proposed in combination with compational approaches seeking the projection that maximizes such indices; two classical projection non-normality measures are the moment-based skewness and kurtosis. We explore the PP problem employing these measures, under the assumption that the underlying multivariate model belongs to the family of scale mixtrues of skew-normal (SMSN) distributions, and show that PP outcomes have close connections with the shape vector of the underlying model. Our findings hint a new way to interpret PP methods, when they are considered under well-established multivariate parametric distributions, an issue which points out relevant implications in the statistical practice.
Palabras clave: Projection pursuit skewness kurtosis scale mixtures of skew-normal distributions