|Abstract:|| We consider the problem of testing a generalized linear model (GLM) with possibly misspecified distribution. In this case, the traditional tests lose their good properties, since the Fisher information is estimated under incorrect assumptions. Here we present a testing approach that is based on random sign-flipping of score contributions, while not requiring any estimate of the Fisher information. As long as the link function is correct and under mild assumptions, our method is robust (i.e. asymptotically exact, consist) against several types of model misspecification, such as overdispersion, heteroscedasticity and, in some cases, ignored nuisance parameters. Among the other features, the methods extends easily to the multivariate (and multiple testing) framework, since it deals efficiently with the dependence of univariate tests without the need of estimating it. Some application to real data is shown and discussed.
Based on joint work with Jesse Hemerik and Jelle Goeman