Data depth and rank-based tests for covariance and spectral density matrices

Handle URI:
http://hdl.handle.net/10754/626479
Title:
Data depth and rank-based tests for covariance and spectral density matrices
Authors:
Chau, Joris; Ombao, Hernando; Sachs, Rainer von
Abstract:
In multivariate time series analysis, objects of primary interest to study cross-dependences in the time series are the autocovariance or spectral density matrices. Non-degenerate covariance and spectral density matrices are necessarily Hermitian and positive definite, and our primary goal is to develop new methods to analyze samples of such matrices. The main contribution of this paper is the generalization of the concept of statistical data depth for collections of covariance or spectral density matrices by exploiting the geometric properties of the space of Hermitian positive definite matrices as a Riemannian manifold. This allows one to naturally characterize most central or outlying matrices, but also provides a practical framework for rank-based hypothesis testing in the context of samples of covariance or spectral density matrices. First, the desired properties of a data depth function acting on the space of Hermitian positive definite matrices are presented. Second, we propose two computationally efficient pointwise and integrated data depth functions that satisfy each of these requirements. Several applications of the developed methodology are illustrated by the analysis of collections of spectral matrices in multivariate brain signal time series datasets.
KAUST Department:
Applied Mathematics and Computational Science Program
Publisher:
arXiv
Issue Date:
26-Jun-2017
ARXIV:
arXiv:1706.08289
Type:
Preprint
Additional Links:
http://arxiv.org/abs/1706.08289v2; http://arxiv.org/pdf/1706.08289v2
Appears in Collections:
Other/General Submission; Applied Mathematics and Computational Science Program

Full metadata record

DC FieldValue Language
dc.contributor.authorChau, Jorisen
dc.contributor.authorOmbao, Hernandoen
dc.contributor.authorSachs, Rainer vonen
dc.date.accessioned2017-12-28T07:32:12Z-
dc.date.available2017-12-28T07:32:12Z-
dc.date.issued2017-06-26en
dc.identifier.urihttp://hdl.handle.net/10754/626479-
dc.description.abstractIn multivariate time series analysis, objects of primary interest to study cross-dependences in the time series are the autocovariance or spectral density matrices. Non-degenerate covariance and spectral density matrices are necessarily Hermitian and positive definite, and our primary goal is to develop new methods to analyze samples of such matrices. The main contribution of this paper is the generalization of the concept of statistical data depth for collections of covariance or spectral density matrices by exploiting the geometric properties of the space of Hermitian positive definite matrices as a Riemannian manifold. This allows one to naturally characterize most central or outlying matrices, but also provides a practical framework for rank-based hypothesis testing in the context of samples of covariance or spectral density matrices. First, the desired properties of a data depth function acting on the space of Hermitian positive definite matrices are presented. Second, we propose two computationally efficient pointwise and integrated data depth functions that satisfy each of these requirements. Several applications of the developed methodology are illustrated by the analysis of collections of spectral matrices in multivariate brain signal time series datasets.en
dc.publisherarXiven
dc.relation.urlhttp://arxiv.org/abs/1706.08289v2en
dc.relation.urlhttp://arxiv.org/pdf/1706.08289v2en
dc.rightsArchived with thanks to arXiven
dc.titleData depth and rank-based tests for covariance and spectral density matricesen
dc.typePreprinten
dc.contributor.departmentApplied Mathematics and Computational Science Programen
dc.eprint.versionPre-printen
dc.contributor.institutionInstitute of Statistics, Biostatistics, and Actuarial Sciences, Universite catholique de Louvain, Voie du Roman Pays 20, B-1348, Louvain-la-Neuve, Belgium.en
dc.contributor.institutionDepartment of Statistics, University of California at Irvine, Bren Hall 2206, Irvine, CA, 92697, United Statesen
dc.identifier.arxividarXiv:1706.08289en
kaust.authorOmbao, Hernandoen
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