  Generalized linear models are often misspecified due to overdispersion,
heteroscedasticity and ignored nuisance variables. Existing quasi-likelihood
methods for testing in misspecified models often do not provide satisfactory
type-I error rate control. We provide a novel semi-parametric test, based on
sign-flipping individual score contributions. The tested parameter is allowed
to be multi-dimensional and even high-dimensional. Our test is often robust
against the mentioned forms of misspecification and provides better type-I
error control than its competitors. When nuisance parameters are estimated, our
basic test becomes conservative. We show how to take nuisance estimation into
account to obtain an asymptotically exact test. Our proposed test is
asymptotically equivalent to its parametric counterpart.

Methodology