Title: Maximal skewness projections for scale mixtures of skew-normal vectors
Authors: Jorge Martin Arevalillo - UNED (Spain) [presenting]
Hilario Navarro-Veguillas - UNED / Facultad de Ciencias (Spain)
Abstract: Multivariate scale mixtures of skew-normal (SMSN) variables are flexible models that account for non-normality in multivariate data scenarios by tail weight assessment and a shape vector representing the asymmetry of the model in a directional fashion. Its stochastic representation involves a skew-normal (SN) vector and a non negative mixing scalar variable, independent of the SN vector, that injects kurtosis into the SMSN model. We address the problem of finding the maximal skewness projection for vectors that follow a SMSN distribution; when simple conditions on the moments of the mixing variable are fulfilled, it can be shown that the direction yielding the maximal skewness is proportional to the shape vector. This finding stresses the directional nature of the asymmetry in this class of distributions; it also provides the theoretical underpinnings for skewness based projection pursuit under a general and flexible class of multivariate distributions. Some examples that show the validity of our result for some widely used distributions within the SMSN family are also given.