Simplicial band depth for multivariate functional data

Handle URI:
http://hdl.handle.net/10754/563434
Title:
Simplicial band depth for multivariate functional data
Authors:
López-Pintado, Sara; Sun, Ying ( 0000-0001-6703-4270 ) ; Lin, Juan K.; Genton, Marc G. ( 0000-0001-6467-2998 )
Abstract:
We propose notions of simplicial band depth for multivariate functional data that extend the univariate functional band depth. The proposed simplicial band depths provide simple and natural criteria to measure the centrality of a trajectory within a sample of curves. Based on these depths, a sample of multivariate curves can be ordered from the center outward and order statistics can be defined. Properties of the proposed depths, such as invariance and consistency, can be established. A simulation study shows the robustness of this new definition of depth and the advantages of using a multivariate depth versus the marginal depths for detecting outliers. Real data examples from growth curves and signature data are used to illustrate the performance and usefulness of the proposed depths. © 2014 Springer-Verlag Berlin Heidelberg.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division; Applied Mathematics and Computational Science Program; Spatio-Temporal Statistics and Data Analysis Group
Publisher:
Springer Nature
Journal:
Advances in Data Analysis and Classification
Issue Date:
5-Mar-2014
DOI:
10.1007/s11634-014-0166-6
Type:
Article
ISSN:
18625347
Appears in Collections:
Articles; Applied Mathematics and Computational Science Program; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorLópez-Pintado, Saraen
dc.contributor.authorSun, Yingen
dc.contributor.authorLin, Juan K.en
dc.contributor.authorGenton, Marc G.en
dc.date.accessioned2015-08-03T11:51:22Zen
dc.date.available2015-08-03T11:51:22Zen
dc.date.issued2014-03-05en
dc.identifier.issn18625347en
dc.identifier.doi10.1007/s11634-014-0166-6en
dc.identifier.urihttp://hdl.handle.net/10754/563434en
dc.description.abstractWe propose notions of simplicial band depth for multivariate functional data that extend the univariate functional band depth. The proposed simplicial band depths provide simple and natural criteria to measure the centrality of a trajectory within a sample of curves. Based on these depths, a sample of multivariate curves can be ordered from the center outward and order statistics can be defined. Properties of the proposed depths, such as invariance and consistency, can be established. A simulation study shows the robustness of this new definition of depth and the advantages of using a multivariate depth versus the marginal depths for detecting outliers. Real data examples from growth curves and signature data are used to illustrate the performance and usefulness of the proposed depths. © 2014 Springer-Verlag Berlin Heidelberg.en
dc.publisherSpringer Natureen
dc.subjectBand depthen
dc.subjectFunctional and image dataen
dc.subjectFunctional boxploten
dc.subjectModified band depthen
dc.subjectMultivariateen
dc.subjectSimplicialen
dc.titleSimplicial band depth for multivariate functional dataen
dc.typeArticleen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.contributor.departmentApplied Mathematics and Computational Science Programen
dc.contributor.departmentSpatio-Temporal Statistics and Data Analysis Groupen
dc.identifier.journalAdvances in Data Analysis and Classificationen
dc.contributor.institutionDepartment of Biostatistics, Columbia University, NY, NY, 10032, United Statesen
dc.contributor.institutionDepartment of Statistics, The Ohio State University, Columbus, OH, 43210, United Statesen
dc.contributor.institutionSearchForce, Inc., San Mateo, CA, 94403, United Statesen
kaust.authorGenton, Marc G.en
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