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dc.contributor.authorPardo Fernández, Juan Carlos
dc.contributor.authorKeilegom, Ingrid van
dc.contributor.authorGonzález Manteiga, Wenceslao
dc.date.accessioned2019-04-09T07:16:32Z
dc.date.available2019-04-09T07:16:32Z
dc.date.issued2007
dc.identifier.citationPardo-Fernández, J. C., Van Keilegom, I. & González-Manteiga, W. (2007). Testing for the equality of k regression curves. Statistica Sinica. Vol. 17, n. 3, pp. 1115-1137
dc.identifier.issn1017-0405
dc.identifier.urihttp://hdl.handle.net/10347/18560
dc.description.abstractAssume that (Xj , Yj ) are independent random vectors satisfying the nonparametric regression models Yj = mj (Xj ) + σj (Xj )εj , for j = 1, . . . , k, where mj (Xj ) = E(Yj |Xj ) and σ 2 j (Xj ) = Var (Yj |Xj ) are smooth but unknown regression and variance functions respectively, and the error variable εj is independent of Xj . In this article we introduce a procedure to test the hypothesis of equality of the k regression functions. The test is based on the comparison of two estimators of the distribution of the errors in each population. Kolmogorov-Smirnov and Cram´er-von Mises type statistics are considered, and their asymptotic distributions are obtained. The proposed tests can detect local alternatives converging to the null hypothesis at the rate n −1/2 . We describe a bootstrap procedure that approximates the critical values, and present the results of a simulation study in which the behavior of the tests for small and moderate sample sizes is studied. Finally, we include an application to a data set
dc.description.sponsorshipThe research of Juan Carlos Pardo-Fernández is supported by Ministerio de Educación y Ciencia (project MTM2005-00820, with additional European FEDER support), Vicerreitorado de Investigación of the Universidade de Vigo and Dirección Xeral de Investigación e Desenvolvemento of the Xunta de Galicia. The research of Ingrid Van Keilegom is supported by IAP research network nr. P5/24 of the Belgian government (Belgian Science Policy). The research of Wenceslao González-Manteiga is supported Ministerio de Educación y Ciencia (project MTM2005-00820, with additional European FEDER support) and Xunta de Galicia (project PGIDIT03PXIC20702PN)
dc.language.isoeng
dc.publisherAcademia Sinica, Institute of Statistical Science
dc.rights© 2007 Academia Sinica, Institute of Statistical Science
dc.subjectBootstrap
dc.subjectComparison of regression curves
dc.subjectHeteroscedastic regression
dc.subjectNonparametric regression
dc.titleTesting for the equality of k regression curves
dc.typejournal article
dc.relation.publisherversionhttp://www3.stat.sinica.edu.tw/statistica/J17N3/J17N315/J17N315.html
dc.type.hasVersionVoR
dc.identifier.essn1996-8507
dc.rights.accessRightsopen access
dc.contributor.affiliationUniversidade de Santiago de Compostela. Departamento de Estatística, Análise Matemática e Optimización
dc.description.peerreviewedSI


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