Title: Robust testing in generalized linear models by sign-flipping score contributions
Authors: Livio Finos - University of Padova (Italy) [presenting]
Abstract: 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 present a novel semi-parametric test, based on sign-flipping individual score contributions that is proven to be robust against variance misspecification. 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. The speed of convergence can be further accelerated considering a particular transformation of the contributions of the score that makes them independent. With this transformation, the test shows an excellent control of the first type error, even for very low sample size and nuisances parameters strongly correlated with the tested parameter. The advantage with respect to other methods is further magnified when the method is extended to the multi-dimensional and even high-dimensional setting. The presented approach is very flexible. We show natural extensions to more complex models, such as random effect models and penalized models.