Testing Additivity in Generalized Nonparametric Regression Models

We develop kernel-based consistent tests of an hypothesis of additivity in nonparametric regression extending recent work on testing parametric null hypotheses against nonparametric alternatives. The additivity hypothesis is of interest because it delivers interpretability and reasonably fast convergence rates for standard estimators. The asymptotic distributions of the tests under a sequence of local alternatives are found and compared: in fact, we give a ranking of the different tests based on local asymptotic power. The practical performance is investigated via simulations and an application to the German migration data of Linton and Härdle (1996).