RT Journal Article
T1 Testing for the equality of k regression curves
A1 Pardo Fernández, Juan Carlos
A1 Keilegom, Ingrid van
A1 González Manteiga, Wenceslao
K1 Bootstrap
K1 Comparison of regression curves
K1 Heteroscedastic regression
K1 Nonparametric regression
AB Assume that (Xj , Yj ) are independent random vectors satisfying the nonparametric regression models Yj = mj (Xj ) + σj (Xj )εj , for j = 1, . . . , k, wheremj (Xj ) = E(Yj |Xj ) and σ2j (Xj ) = Var (Yj |Xj ) are smooth but unknown regressionand 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 ofthe k regression functions. The test is based on the comparison of two estimators of the distribution of the errors in each population. Kolmogorov-Smirnov andCram´er-von Mises type statistics are considered, and their asymptotic distributionsare obtained. The proposed tests can detect local alternatives converging to thenull 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 whichthe behavior of the tests for small and moderate sample sizes is studied. Finally,we include an application to a data set
PB Academia Sinica, Institute of Statistical Science
SN 1017-0405
YR 2007
FD 2007
LK http://hdl.handle.net/10347/18560
UL http://hdl.handle.net/10347/18560
LA eng
NO 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
NO The research of Juan Carlos Pardo-Fernández is supported by Ministeriode Educación y Ciencia (project MTM2005-00820, with additional EuropeanFEDER support), Vicerreitorado de Investigación of the Universidade de Vigoand 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 researchof Wenceslao González-Manteiga is supported Ministerio de Educación y Ciencia (project MTM2005-00820, with additional European FEDER support) andXunta de Galicia (project PGIDIT03PXIC20702PN)
DS Minerva
RD 28 abr 2026