Testing Generalized Linear and Semiparametric Models Against Smooth Alternatives

We propose goodness of t 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 coe cient models as proposed by Hastie Tibshirani 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 p n power but in contrast to parametric tests it is powerful against smooth alternatives in general