A characterization of elliptical distributions and some optimality properties of principal components for functional data

dc.creatorBoente Boente, Graciela Lina
dc.creatorSalibian Barrera, Matías Octavio
dc.creatorTyler, David E.
dc.date2014-10
dc.identifierhttp://hdl.handle.net/11336/18730
dc.identifierBoente Boente, Graciela Lina; Salibian Barrera, Matías Octavio; Tyler, David E.; A characterization of elliptical distributions and some optimality properties of principal components for functional data; Elsevier Inc; Journal Of Multivariate Analysis; 131; 10-2014; 254-264
dc.identifier0047-259X
dc.identifierCONICET Digital
dc.identifierCONICET
dc.descriptionAs in the multivariate setting, the class of elliptical distributions on separable Hilbert spaces serves as an important vehicle and reference point for the development and evaluation of robust methods in functional data analysis. In this paper, we present a simple characterization of elliptical distributions on separable Hilbert spaces, namely we show that the class of elliptical distributions in the infinite-dimensional case is equivalent to the class of scale mixtures of Gaussian distributions on the space. Using this characterization, we establish a stochastic optimality property for the principal component subspaces associated with an elliptically distributed random element, which holds even when second moments do not exist. In addition, when second moments exist, we establish an optimality property regarding unitarily invariant norms of the residuals covariance operator.
dc.descriptionFil: Boente Boente, Graciela Lina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santalo". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santalo"; Argentina
dc.descriptionFil: Salibian Barrera, Matías Octavio. University Of British Columbia; Canadá
dc.descriptionFil: Tyler, David E.. Rutgers University; Estados Unidos
dc.formatapplication/pdf
dc.formatapplication/pdf
dc.languageeng
dc.publisherElsevier Inc
dc.relationinfo:eu-repo/semantics/altIdentifier/doi/10.1016/j.jmva.2014.07.006
dc.relationinfo:eu-repo/semantics/altIdentifier/url/http://www.sciencedirect.com/science/article/pii/S0047259X14001638
dc.rightsinfo:eu-repo/semantics/openAccess
dc.rightshttps://creativecommons.org/licenses/by-nc-nd/2.5/ar/
dc.subjectElliptical Distributions
dc.subjectFunctional Data Analysis
dc.subjectPrincipal Components
dc.subjecthttps://purl.org/becyt/ford/1.1
dc.subjecthttps://purl.org/becyt/ford/1
dc.titleA characterization of elliptical distributions and some optimality properties of principal components for functional data
dc.typeinfo:eu-repo/semantics/article
dc.typeinfo:ar-repo/semantics/artículo
dc.typeinfo:eu-repo/semantics/publishedVersion


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