Testing additivity in generalized nonparametric regression models with estimated parameters

We develop several kernel-based consistent tests of an hypothesis of additivity in nonparametric regression. We allow for discrete covariates and parameters estimated from a semiparametric GMM criterion function. The additivity hypothesis is of interest because it delivers interpretability and reasonably fast convergence rates for nonparametric estimators. The asymptotic distribution of the parameter estimators are found. We also derive the asymptotic distribution of the additivity test statistics under a sequence of local alternatives. We give a ranking of the different tests based on local asymptotic power. The practical performance is investigated through simulations based on the data set used in Linton and Hنrdle (1996).