Projection Pursuit mediante un enfoque paramétrico basado en distribuciones multivariantes con asimetría y kurtosis

J. Martín Arevalillo, H. Navarro Veguillas

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.

Keywords: Projection pursuit, skewness, kurtosis, scale mixtures of skew-normal distributions

Multivariate Analysis
September 2, 2026  3:30 PM
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