Testing for the equality of k regression curves. Stat. Sin
AbstractAssume that (X-j, Y-j) are independent random vectors satisfying the nonparametric regression models Y-j = m(j) (X-j) + sigma(j) (X-j)epsilon(j), for j = 1, ... , k, where mj (X-j) = E(Y-j | X-j) and sigma(2)(j)(X-j) = Var (Y-j | X-j) are smooth but unknown regression and variance functions respectively, and the error variable epsilon(j) is independent of X-j. 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 Cramer-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.
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Bibliographic InfoPaper provided by Université catholique de Louvain in its series Open Access publications from Université catholique de Louvain with number info:hdl:2078.1/37404.
Date of creation: 2007
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Publication status: Published in Statistica Sinica (2007) v.17, p.1115-1137
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Web page: http://www.uclouvain.be
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- Michael G. Akritas, 2001. "Non-parametric Estimation of the Residual Distribution," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics & Finnish Statistical Society & Norwegian Statistical Association & Swedish Statistical Association, vol. 28(3), pages 549-567.
- Delgado, Miguel A., .
"Testing the Equality of Nonparametric Regression Curves,"
Open Access publications from Universidad Carlos III de Madrid
info:hdl:10016/2389, Universidad Carlos III de Madrid.
- Delgado, Miguel A., 1993. "Testing the equality of nonparametric regression curves," Statistics & Probability Letters, Elsevier, vol. 17(3), pages 199-204, June.
- Delgado, Miguel A., . "Testing the equality of nonparametric regression curves," Open Access publications from Universidad Carlos III de Madrid info:hdl:10016/2826, Universidad Carlos III de Madrid.
- repec:ner:louvai:info:hdl:2078.1/59436 is not listed on IDEAS
- Miguel A. Delgado & Juan Carlos Escanciano, 2011.
"Conditional stochastic dominance testing,"
Economics Working Papers
we1138, Universidad Carlos III, Departamento de Economía.
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