Kauermann, Göran and Tutz, Gerhard
Testing Generalized Linear and Semiparametric Models Against Smooth Alternatives.
Collaborative Research Center 386, Discussion Paper 149
We propose goodness of fit tests for testing generalized linear models and semiparametric regression models against smooth alternatives. The focus is on models having both, continuous and factorial covariates. As smooth extension of a parametric or semiparametric model we use generalized varying coefficient models as proposed by Hastie&Tibshirani (JRSS B, 1993). A likelihood ratio statistic is used for testing, and asymptotic normality of the test statistic is proven. Due to a slow asymptotic convergence rate a bootstrap approach is pursued. Asymptotic expansions allow to write the estimates as linear smoothers which in turn guarantees simple and fast bootstrapping. The test is shown to have sqrt(n) power, but in contrast to parametric tests it is powerful against smooth alternatives in general.