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Equivalent kernels of smoothing splines in nonparametric regression for clustered/longitudinal data

Lin, Xihong; Wang, Naisyin; Welsh, Alan; Carroll, Raymond

Description

For independent data, it is well known that kernel methods and spline methods are essentially asymptotically equivalent (Silverman, 1984). However, recent work of Welsh et al. (2002) shows that the same is not true for clustered/longitudinal data. Splines and conventional kernels are different in localness and ability to account for the within-cluster correlation. We show that a smoothing spline estimator is asymptotically equivalent to a recently proposed seemingly unrelated kernel estimator...[Show more]

dc.contributor.authorLin, Xihong
dc.contributor.authorWang, Naisyin
dc.contributor.authorWelsh, Alan
dc.contributor.authorCarroll, Raymond
dc.date.accessioned2015-12-13T22:42:06Z
dc.date.available2015-12-13T22:42:06Z
dc.identifier.issn0006-3444
dc.identifier.urihttp://hdl.handle.net/1885/78821
dc.description.abstractFor independent data, it is well known that kernel methods and spline methods are essentially asymptotically equivalent (Silverman, 1984). However, recent work of Welsh et al. (2002) shows that the same is not true for clustered/longitudinal data. Splines and conventional kernels are different in localness and ability to account for the within-cluster correlation. We show that a smoothing spline estimator is asymptotically equivalent to a recently proposed seemingly unrelated kernel estimator of Wang (2003) for any working covariance matrix. We show that both estimators can be obtained iteratively by applying conventional kernel or spline smoothing to pseudo-observations. This result allows us to study the asymptotic properties of the smoothing spline estimator by deriving its asymptotic bias and variance. We show that smoothing splines are consistent for an arbitrary working covariance and have the smallest variance when assuming the true covariance. We further show that both the seemingly unrelated kernel estimator and the smoothing spline estimator are nonlocal unless working independence is assumed but have asymptotically negligible bias. Their finite sample performance is compared through simulations. Our results justify the use of efficient, non-local estimators such as smoothing splines for clustered/longitudinal data.
dc.publisherBiometrika Trust
dc.sourceBiometrika
dc.subjectKeywords: Asymptotic bias and variance; Asymptotic equivalent kernel; Consistency; Kernel regression; Longitudinal data; Non-localness; Nonparametric regression; Smoothing spline regression
dc.titleEquivalent kernels of smoothing splines in nonparametric regression for clustered/longitudinal data
dc.typeJournal article
local.description.notesImported from ARIES
local.description.refereedYes
local.identifier.citationvolume91
dc.date.issued2004
local.identifier.absfor010405 - Statistical Theory
local.identifier.ariespublicationMigratedxPub7389
local.type.statusPublished Version
local.contributor.affiliationLin, Xihong, University of Michigan
local.contributor.affiliationWang, Naisyin, Texas A&M University
local.contributor.affiliationWelsh, Alan, College of Physical and Mathematical Sciences, ANU
local.contributor.affiliationCarroll, Raymond, Texas A&M University
local.bibliographicCitation.issue1
local.bibliographicCitation.startpage177
local.bibliographicCitation.lastpage193
local.identifier.doi10.1093/biomet/91.1.177
dc.date.updated2015-12-11T10:05:37Z
local.identifier.scopusID2-s2.0-3543023777
CollectionsANU Research Publications

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