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dc.contributor.author | Pardo Fernández, Juan Carlos |
dc.contributor.author | Keilegom, Ingrid van |
dc.contributor.author | González Manteiga, Wenceslao |
dc.date.accessioned | 2019-04-09T07:16:32Z |
dc.date.available | 2019-04-09T07:16:32Z |
dc.date.issued | 2007 |
dc.identifier.citation | Pardo-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.issn | 1017-0405 |
dc.identifier.uri | http://hdl.handle.net/10347/18560 |
dc.description.abstract | Assume 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.sponsorship | The 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.iso | eng |
dc.publisher | Academia Sinica, Institute of Statistical Science |
dc.rights | © 2007 Academia Sinica, Institute of Statistical Science |
dc.subject | Bootstrap |
dc.subject | Comparison of regression curves |
dc.subject | Heteroscedastic regression |
dc.subject | Nonparametric regression |
dc.title | Testing for the equality of k regression curves |
dc.type | journal article |
dc.relation.publisherversion | http://www3.stat.sinica.edu.tw/statistica/J17N3/J17N315/J17N315.html |
dc.type.hasVersion | VoR |
dc.identifier.essn | 1996-8507 |
dc.rights.accessRights | open access |
dc.contributor.affiliation | Universidade de Santiago de Compostela. Departamento de Estatística, Análise Matemática e Optimización |
dc.description.peerreviewed | SI |
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