Exact fast computation of band depth for large functional datasets: How quickly can one million curves be ranked?

Handle URI:
http://hdl.handle.net/10754/598262
Title:
Exact fast computation of band depth for large functional datasets: How quickly can one million curves be ranked?
Authors:
Sun, Ying; Genton, Marc G.; Nychka, Douglas W.
Abstract:
© 2012 John Wiley & Sons, Ltd. Band depth is an important nonparametric measure that generalizes order statistics and makes univariate methods based on order statistics possible for functional data. However, the computational burden of band depth limits its applicability when large functional or image datasets are considered. This paper proposes an exact fast method to speed up the band depth computation when bands are defined by two curves. Remarkable computational gains are demonstrated through simulation studies comparing our proposal with the original computation and one existing approximate method. For example, we report an experiment where our method can rank one million curves, evaluated at fifty time points each, in 12.4 seconds with Matlab.
Citation:
Sun Y, Genton MG, Nychka DW (2012) Exact fast computation of band depth for large functional datasets: How quickly can one million curves be ranked? Stat 1: 68–74. Available: http://dx.doi.org/10.1002/sta4.8.
Publisher:
Wiley-Blackwell
Journal:
Stat
KAUST Grant Number:
KUS-C1-016-04
Issue Date:
Oct-2012
DOI:
10.1002/sta4.8
Type:
Article
ISSN:
2049-1573
Sponsors:
This research was partially supported by NSF grants DMS-1007504, DMS-1106494, and by Award No. KUS-C1-016-04 made by King Abdullah University of Science and Technology (KAUST).
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Full metadata record

DC FieldValue Language
dc.contributor.authorSun, Yingen
dc.contributor.authorGenton, Marc G.en
dc.contributor.authorNychka, Douglas W.en
dc.date.accessioned2016-02-25T13:17:36Zen
dc.date.available2016-02-25T13:17:36Zen
dc.date.issued2012-10en
dc.identifier.citationSun Y, Genton MG, Nychka DW (2012) Exact fast computation of band depth for large functional datasets: How quickly can one million curves be ranked? Stat 1: 68–74. Available: http://dx.doi.org/10.1002/sta4.8.en
dc.identifier.issn2049-1573en
dc.identifier.doi10.1002/sta4.8en
dc.identifier.urihttp://hdl.handle.net/10754/598262en
dc.description.abstract© 2012 John Wiley & Sons, Ltd. Band depth is an important nonparametric measure that generalizes order statistics and makes univariate methods based on order statistics possible for functional data. However, the computational burden of band depth limits its applicability when large functional or image datasets are considered. This paper proposes an exact fast method to speed up the band depth computation when bands are defined by two curves. Remarkable computational gains are demonstrated through simulation studies comparing our proposal with the original computation and one existing approximate method. For example, we report an experiment where our method can rank one million curves, evaluated at fifty time points each, in 12.4 seconds with Matlab.en
dc.description.sponsorshipThis research was partially supported by NSF grants DMS-1007504, DMS-1106494, and by Award No. KUS-C1-016-04 made by King Abdullah University of Science and Technology (KAUST).en
dc.publisherWiley-Blackwellen
dc.subjectApproximate solutionen
dc.subjectBand depthen
dc.subjectExact solutionen
dc.subjectFunctional boxploten
dc.subjectFunctional dataen
dc.subjectLarge dataseten
dc.subjectModified band depthen
dc.titleExact fast computation of band depth for large functional datasets: How quickly can one million curves be ranked?en
dc.typeArticleen
dc.identifier.journalStaten
dc.contributor.institutionDepartment of Statistics; University of Chicago; Chicago IL 60637 USAen
dc.contributor.institutionDepartment of Statistics; Texas A&M University; College Station TX 77843-3143 USAen
dc.contributor.institutionGeophysical Statistics Project; National Center for Atmospheric Research; Boulder CO 80307-3000 USAen
kaust.grant.numberKUS-C1-016-04en
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