Asymptotics for general multivariate kernel density derivative estimators

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dc.contributor.author Chacon, JE
dc.contributor.author Duong, T
dc.contributor.author Wand, M
dc.date.accessioned 2012-10-12T03:32:47Z
dc.date.issued 2011-01
dc.identifier.citation Statistica Sinica, 2011, 21 pp. 807 - 840
dc.identifier.issn 1017-0405
dc.identifier.other C1UNSUBMIT en_US
dc.identifier.uri http://hdl.handle.net/10453/17935
dc.description.abstract We investigate kernel estimators of multivariate density derivative functions using general (or unconstrained) bandwidth matrix selectors. These density derivative estimators have been relatively less well researched than their density estimator analogues. A major obstacle for progress has been the intractability of the matrix analysis when treating higher order multivariate derivatives. With an alternative vectorization of these higher order derivatives, mathematical intractabilities are surmounted in an elegant and unified framework. The finite sample and asymptotic analysis of squared errors for density estimators are generalized to density derivative estimators. Moreover, we are able to exhibit a closed form expression for a normal scale bandwidth matrix for density derivative estimators. These normal scale bandwidths are employed in a numerical study to demonstrate the gain in performance of unconstrained selectors over their constrained counterparts.
dc.publisher Academia Sinica
dc.title Asymptotics for general multivariate kernel density derivative estimators
dc.type Journal Article
dc.description.version Published
dc.parent Statistica Sinica
dc.journal.volume 21
dc.journal.number en_US
dc.publocation Taiwan en_US
dc.identifier.startpage 807 en_US
dc.identifier.endpage 840 en_US
dc.cauo.name SCI.Mathematical Sciences en_US
dc.conference Verified OK en_US
dc.for 0101 Pure Mathematics
dc.personcode 110509
dc.percentage 100 en_US
dc.classification.name Pure Mathematics en_US
dc.classification.type FOR-08 en_US
dc.edition en_US
dc.custom en_US
dc.date.activity en_US
dc.location.activity en_US
dc.description.keywords Asymptotic mean integrated squared error
dc.description.keywords normal scale rule
dc.description.keywords optimal
dc.description.keywords unconstrained bandwidth matrices
pubs.embargo.period Not known
pubs.organisational-group /University of Technology Sydney
pubs.organisational-group /University of Technology Sydney/Faculty of Science
utslib.copyright.status Open Access
utslib.copyright.date 2015-04-15 12:23:47.074767+10
pubs.consider-herdc false
utslib.collection.history General (ID: 2)
utslib.collection.history School of Mathematical Sciences (ID: 340)


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