A powerful test for comparing multiple regression functions

In this article, we address the important problem of comparison of two or more population regression functions. Recently, Pardo-Fernández, Van Keilegom and González-Manteiga [2007, ‘Testing for Equality of k Regression Curves’, Statistica Sinica, 17, 1115–1137] developed test statistics for simple nonparametric regression models: Yij=θj(Zij)+σj(Zij)εij, based on empirical distributions of the errors in each population j=1, …, J. In this article, we propose a test for equality of the θj(·) based on the concept of generalised likelihood ratio type statistics. We also generalise our test for other nonparametric regression set-ups, for example, nonparametric logistic regression, where the log-likelihood for population j is any general smooth function ℒ{Yj, θj(Zj)}. We describe a resampling procedure to obtain the critical values of the test. In addition, we present a simulation study to evaluate the performance of the proposed test and compare our results to those in Pardo-Fernández et al. [2007, ‘Testing for Equality of k Regression Curves’, Statistica Sinica, 17, 1115–1137].