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The shattering dimension of sets of linear functionals

Schechtman, Gideon; Mendelson, Shahar

Description

We evaluate the shattering dimension of various classes of linear functionals on various symmetric convex sets. The proofs here relay mostly on methods from the local theory of normed spaces and include volume estimates, factorization techniques and tail estimates of norms, viewed as random variables on Euclidean spheres. The estimates of shattering dimensions can be applied to obtain error bounds for certain classes of functions, a fact which was the original motivation of this study....[Show more]

dc.contributor.authorSchechtman, Gideon
dc.contributor.authorMendelson, Shahar
dc.date.accessioned2016-03-04T01:39:19Z
dc.date.available2016-03-04T01:39:19Z
dc.identifier.issn0091-1798
dc.identifier.urihttp://hdl.handle.net/1885/100163
dc.description.abstractWe evaluate the shattering dimension of various classes of linear functionals on various symmetric convex sets. The proofs here relay mostly on methods from the local theory of normed spaces and include volume estimates, factorization techniques and tail estimates of norms, viewed as random variables on Euclidean spheres. The estimates of shattering dimensions can be applied to obtain error bounds for certain classes of functions, a fact which was the original motivation of this study. Although this can probably be done in a more traditional manner, we also use the approach presented here to determine whether several classes of linear functionals satisfy the uniform law of large numbers and the uniform central limit theorem.
dc.publisherInstitute of Mathematical Statistics
dc.rights© Institute of Mathematical Statistics, 2004. http://www.sherpa.ac.uk/romeo/issn/0091-1798..."author can archive publisher's version/PDF. On author's personal website or open access repository" from SHERPA/RoMEO site (as at 4/03/16).
dc.sourceThe Annals of Probability
dc.subjectKeywords: Empirical processes; Linear functionals; Shattering dimension
dc.titleThe shattering dimension of sets of linear functionals
dc.typeJournal article
local.description.notesImported from ARIES
local.description.refereedYes
local.identifier.citationvolume32
dc.date.issued2004
local.identifier.absfor080109
local.identifier.ariespublicationMigratedxPub16575
local.publisher.urlhttp://imstat.org/en/index.html
local.type.statusPublished Version
local.contributor.affiliationMendelson, Shahar, College of Engineering and Computer Science, College of Engineering and Computer Science, Research School of Computer Science, The Australian National University
local.contributor.affiliationSchechtman, Gideon, Weizmann Institute of Science, Israel
local.bibliographicCitation.issue3A
local.bibliographicCitation.startpage1746
local.bibliographicCitation.lastpage1770
local.identifier.doi10.1214/009117904000000388
dc.date.updated2016-06-14T08:37:15Z
local.identifier.scopusID2-s2.0-4544289259
dcterms.accessRightsOpen Access
CollectionsANU Research Publications

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