Smoothing splines with varying smoothing parameter

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dc.contributor.authorWang, X.en
dc.contributor.authorDu, P.en
dc.contributor.authorShen, J.en
dc.contributor.departmentStatisticsen
dc.date.accessioned2017-01-23T22:42:46Zen
dc.date.available2017-01-23T22:42:46Zen
dc.date.issued2013-12-01en
dc.description.abstractThis paper considers the development of spatially adaptive smoothing splines for the estimation of a regression function with non-homogeneous smoothness across the domain. Two challenging issues that arise in this context are the evaluation of the equivalent kernel and the determination of a local penalty. The roughness penalty is a function of the design points in order to accommodate local behavior of the regression function. It is shown that the spatially adaptive smoothing spline estimator is approximately a kernel estimator. The resulting equivalent kernel is spatially dependent. The equivalent kernels for traditional smoothing splines are a special case of this general solution. With the aid of the Green’s function for a two-point boundary value problem, the explicit forms of the asymptotic mean and variance are obtained for any interior point. Thus, the optimal roughness penalty function is obtained by approximately minimizing the asymptotic integrated mean square error. Simulation results and an application illustrate the performance of the proposed estimator.en
dc.description.versionPublished versionen
dc.format.extent955 - 970 (16) page(s)en
dc.format.mimetypeapplication/pdfen
dc.identifier.doihttps://doi.org/10.1093/biomet/ast031en
dc.identifier.issn0006-3444en
dc.identifier.issue4en
dc.identifier.urihttp://hdl.handle.net/10919/74410en
dc.identifier.volume100en
dc.language.isoenen
dc.publisherOxford University Pressen
dc.relation.urihttp://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000327714200012&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=930d57c9ac61a043676db62af60056c1en
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectBiologyen
dc.subjectMathematical & Computational Biologyen
dc.subjectStatistics & Probabilityen
dc.subjectLife Sciences & Biomedicine - Other Topicsen
dc.subjectMathematicsen
dc.subjectEquivalent kernelen
dc.subjectGreen's functionen
dc.subjectNonparametric regressionen
dc.subjectSmoothing splineen
dc.subjectSpatially adaptive smoothingen
dc.subjectVARIANCE-FUNCTION ESTIMATIONen
dc.subjectNONPARAMETRIC REGRESSIONen
dc.subjectWAVELET SHRINKAGEen
dc.subjectPOLYNOMIAL SPLINESen
dc.subjectEQUIVALENT KERNELen
dc.subjectADAPTATIONen
dc.subjectSMOOTHNESSen
dc.titleSmoothing splines with varying smoothing parameteren
dc.title.serialBiometrikaen
dc.typeArticle - Refereeden
dc.type.dcmitypeTexten
pubs.organisational-group/Virginia Techen
pubs.organisational-group/Virginia Tech/All T&R Facultyen
pubs.organisational-group/Virginia Tech/Scienceen
pubs.organisational-group/Virginia Tech/Science/COS T&R Facultyen
pubs.organisational-group/Virginia Tech/Science/Statisticsen

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