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Abstract:

As 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. © 2014 Elsevier Inc.

Registro:

Documento: Artículo
Título:A characterization of elliptical distributions and some optimality properties of principal components for functional data
Autor:Boente, G.; Salibián Barrera, M.; Tyler, D.E.
Filiación:Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires and CONICET, Argentina
Department of Statistics, University of British Columbia, Canada
Department of Statistics, Rutgers University, United States
Palabras clave:Elliptical distributions; Functional data analysis; Principal components
Año:2014
Volumen:131
Página de inicio:254
Página de fin:264
DOI: http://dx.doi.org/10.1016/j.jmva.2014.07.006
Título revista:Journal of Multivariate Analysis
Título revista abreviado:J. Multivariate Anal.
ISSN:0047259X
CODEN:JMVAA
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0047259X_v131_n_p254_Boente

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Citas:

---------- APA ----------
Boente, G., Salibián Barrera, M. & Tyler, D.E. (2014) . A characterization of elliptical distributions and some optimality properties of principal components for functional data. Journal of Multivariate Analysis, 131, 254-264.
http://dx.doi.org/10.1016/j.jmva.2014.07.006
---------- CHICAGO ----------
Boente, G., Salibián Barrera, M., Tyler, D.E. "A characterization of elliptical distributions and some optimality properties of principal components for functional data" . Journal of Multivariate Analysis 131 (2014) : 254-264.
http://dx.doi.org/10.1016/j.jmva.2014.07.006
---------- MLA ----------
Boente, G., Salibián Barrera, M., Tyler, D.E. "A characterization of elliptical distributions and some optimality properties of principal components for functional data" . Journal of Multivariate Analysis, vol. 131, 2014, pp. 254-264.
http://dx.doi.org/10.1016/j.jmva.2014.07.006
---------- VANCOUVER ----------
Boente, G., Salibián Barrera, M., Tyler, D.E. A characterization of elliptical distributions and some optimality properties of principal components for functional data. J. Multivariate Anal. 2014;131:254-264.
http://dx.doi.org/10.1016/j.jmva.2014.07.006