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

Arevalillo, Jorge M. y Navarro, Hilario . (2021) Skewness-Based Projection Pursuit as an Eigenvector Problem in Scale Mixtures of Skew-Normal Distributions. Symmetry Volume 13 Issue 6 10.3390/sym13061056

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Título Skewness-Based Projection Pursuit as an Eigenvector Problem in Scale Mixtures of Skew-Normal Distributions
Autor(es) Arevalillo, Jorge M.
Navarro, Hilario
Materia(s) Estadística
Abstract 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.
Palabras clave skewness
scatter matrices
projection pursuit
scale mixtures of skew normal distribution
eigenvector
Editor(es) MDPI
Fecha 2021-06-03
Formato application/pdf
Identificador bibliuned:DptoEOICN-FCIE-Articulos-Hnavarro-00034
http://e-spacio.uned.es/fez/view/bibliuned:DptoEOICN-FCIE-Articulos-Hnavarro-00034
DOI - identifier 10.3390/sym13061056
ISSN - identifier 2073-8994
Nombre de la revista Symmetry
Número de Volumen 13
Número de Issue 16
Publicado en la Revista Symmetry Volume 13 Issue 6 10.3390/sym13061056
Idioma eng
Versión de la publicación acceptedVersion
Tipo de recurso Article
Derechos de acceso y licencia http://creativecommons.org/licenses/by-sa/4.0
info:eu-repo/semantics/openAccess
Tipo de acceso Acceso abierto
Notas adicionales The registered version of this article, first published in Symmetry, is available online at the publisher's website: MDPI, https://doi.org/10.3390/sym13061056
Notas adicionales La versión registrada de este artículo, publicado por primera vez en Symmetry, está disponible en línea en el sitio web del editor: MDPI, https://doi.org/10.3390/sym13061056

 
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Creado: Mon, 29 Jan 2024, 21:30:34 CET