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Data projections by skewness maximization under scale mixtures of skew-normal vectors

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dc.contributor.authorMartín Arevalillo, Jorge
dc.contributor.authorNavarro Veguillas, Hilario
dc.date.accessioned2024-05-20T11:24:49Z
dc.date.available2024-05-20T11:24:49Z
dc.date.issued2020-02-22
dc.description.abstractMultivariate scale mixtures of skew-normal distributions are flexible models that account for the non-normality of data by means of a tail weight parameter and a shape vector representing the asymmetry of the model in a directional fashion. Its stochastic representation involves a skew-normal vector and a non negative mixing scalar variable, independent of the skew-normal vector, that injects tail weight behavior into the model. In this paper we look into the problem of finding the projection that maximizes skewness for vectors that follow a scale mixture of skew-normal distribution; when a simple condition on the moments of the mixing variable is 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 shape vector to regulate the asymmetry; it also provides the theoretical foundations motivating the skewness based projection pursuit problem in this class of distributions. Some examples that illustrate the application of our results are also given; they include a simulation experiment with artificial data, which sheds light on the usefulness and implications of our results, and the application to real data.en
dc.description.versionversión final
dc.identifier.doi10.1007/s11634-020-00388-6
dc.identifier.issn1862-5355
dc.identifier.urihttps://hdl.handle.net/20.500.14468/11928
dc.journal.titleAdvances in Data Analysis and Classification Theory, Methods, and Applications in Data Science
dc.journal.volume14
dc.language.isoen
dc.publisherSpringer
dc.relation.centerFacultad de Ciencias
dc.relation.departmentEstadística, Investigación Operativa y Cálculo Numérico
dc.rightsAtribución-NoComercial-SinDerivadas 4.0 Internacional
dc.rightsinfo:eu-repo/semantics/openAccess
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/4.0
dc.subject.keywordsSkew-normal
dc.subject.keywordsScale mixtures of Skew-normal distributions
dc.subject.keywordsMaximal skewness projection
dc.titleData projections by skewness maximization under scale mixtures of skew-normal vectorses
dc.typeartículoes
dc.typejournal articleen
dspace.entity.typePublication
relation.isAuthorOfPublicationea1c092a-eceb-49c8-abb7-d4d52f53930a
relation.isAuthorOfPublicationb4ef2ce4-140a-4dfd-b87f-363a7a9136e5
relation.isAuthorOfPublication.latestForDiscoveryea1c092a-eceb-49c8-abb7-d4d52f53930a
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