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dc.contributor.authorChau, Joris
dc.contributor.authorOmbao, Hernando
dc.contributor.authorvon Sachs, Rainer
dc.date.accessioned2020-08-17T07:21:18Z
dc.date.available2020-08-17T07:21:18Z
dc.date.issued2019
dc.identifier.citationChau, J., Ombao, H., & Sachs, R. V. (2019). Intrinsic Data Depth for Hermitian Positive Definite Matrices [Data set]. Taylor & Francis. https://doi.org/10.6084/M9.FIGSHARE.7393223.V3
dc.identifier.doi10.6084/m9.figshare.7393223.v3
dc.identifier.urihttp://hdl.handle.net/10754/664622
dc.description.abstractNondegenerate covariance, correlation, and spectral density matrices are necessarily symmetric or Hermitian and positive definite. This article develops statistical data depths for collections of Hermitian positive definite matrices by exploiting the geometric structure of the space as a Riemannian manifold. The depth functions allow one to naturally characterize most central or outlying matrices, but also provide a practical framework for inference in the context of samples of positive definite matrices. First, the desired properties of an intrinsic data depth function acting on the space of Hermitian positive definite matrices are presented. Second, we propose two pointwise and integrated data depth functions that satisfy each of these requirements and investigate several robustness and efficiency aspects. As an application, we construct depth-based confidence regions for the intrinsic mean of a sample of positive definite matrices, which is applied to the exploratory analysis of a collection of covariance matrices in a multicenter clinical trial. Supplementary materials and an accompanying R-package are available online.
dc.publisherTaylor & Francis
dc.subjectNeuroscience
dc.subjectPharmacology
dc.subjectBiotechnology
dc.subjectEvolutionary Biology
dc.subject59999 Environmental Sciences not elsewhere classified
dc.subject69999 Biological Sciences not elsewhere classified
dc.subjectCancer
dc.subjectInorganic Chemistry
dc.subject111714 Mental Health
dc.titleIntrinsic Data Depth for Hermitian Positive Definite Matrices
dc.typeDataset
dc.contributor.departmentBiostatistics Group
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.contributor.departmentStatistics Program
dc.contributor.institutionInstitute of Statistics, Biostatistics, and Actuarial Sciences, Université Catholique de Louvain, Louvain-la-Neuve, Belgium;
dc.contributor.institutionDepartment of Statistics, University of California at Irvine, Irvine, CA;
kaust.personOmbao, Hernando
dc.relation.issupplementtoDOI:10.1080/10618600.2018.1537926
display.relations<b> Is Supplement To:</b><br/> <ul> <li><i>[Article]</i> <br/> Chau J, Ombao H, von Sachs R (2018) Intrinsic Data Depth for Hermitian Positive Definite Matrices. Journal of Computational and Graphical Statistics: 1–25. Available: http://dx.doi.org/10.1080/10618600.2018.1537926.. DOI: <a href="https://doi.org/10.1080/10618600.2018.1537926" >10.1080/10618600.2018.1537926</a> HANDLE: <a href="http://hdl.handle.net/10754/631388">10754/631388</a></li></ul>


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