A characterization of elliptical distributions and some optimality properties of principal components for functional data
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 dis...
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| Formato: | JOUR |
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| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_0047259X_v131_n_p254_Boente |
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todo:paper_0047259X_v131_n_p254_Boente2023-10-03T14:52:21Z A characterization of elliptical distributions and some optimality properties of principal components for functional data Boente, G. Salibián Barrera, M. Tyler, D.E. Elliptical distributions Functional data analysis Principal components 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. Fil:Boente, G. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_0047259X_v131_n_p254_Boente |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-134 |
| collection |
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| topic |
Elliptical distributions Functional data analysis Principal components |
| spellingShingle |
Elliptical distributions Functional data analysis Principal components Boente, G. Salibián Barrera, M. Tyler, D.E. A characterization of elliptical distributions and some optimality properties of principal components for functional data |
| topic_facet |
Elliptical distributions Functional data analysis Principal components |
| description |
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. |
| format |
JOUR |
| author |
Boente, G. Salibián Barrera, M. Tyler, D.E. |
| author_facet |
Boente, G. Salibián Barrera, M. Tyler, D.E. |
| author_sort |
Boente, G. |
| title |
A characterization of elliptical distributions and some optimality properties of principal components for functional data |
| title_short |
A characterization of elliptical distributions and some optimality properties of principal components for functional data |
| title_full |
A characterization of elliptical distributions and some optimality properties of principal components for functional data |
| title_fullStr |
A characterization of elliptical distributions and some optimality properties of principal components for functional data |
| title_full_unstemmed |
A characterization of elliptical distributions and some optimality properties of principal components for functional data |
| title_sort |
characterization of elliptical distributions and some optimality properties of principal components for functional data |
| url |
http://hdl.handle.net/20.500.12110/paper_0047259X_v131_n_p254_Boente |
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| _version_ |
1807319165264986112 |