Testing for the equality of k regression curves
(2004) , 25 pages
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- Authors
- Abstract
- Assume that (Xj , Yj ) are k independent random vectors satisfying the non-parametric regression models Yj= mj (Xj ) + σj (Xj)εj , for j = 1,..., k, where mj (Xj) = E(Yj|Xj) and σ2j (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 H0 : m1 =...= mk 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 Cramér-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 in order to approximate 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 real data set
- Affiliations
Universidade de Vigo Departamento de Estatística e IO Universidade de Santiago de Compostela Departamento de Estatística e IO
Citations
Pardo-Fernández, J. C., Van Keilegom, I., & González - Manteiga, W. (2004). Testing for the equality of k regression curves (STAT Discussion Papers 0416). https://hdl.handle.net/2078.5/32916