Speaker: Jesse Hemerik, University of Oslo (NOR)
Location: Erling Sverdrups plass, Niels Henrik Abels hus, 8th floor
Title: Robust testing in generalized linear models by sign-flipping score contributions
Abstract: Generalized linear models are often misspecified due to overdispersion, heteroscedasticity or 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. (Note that the score, the derivative of the log-likelihood, is the sum of $n$ 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, while having good power.
Our method can be used to obtain robust confidence intervals for parameters in general models and can be extended to mixed models. Moreover, when multiple outcome variables are considered, our test can be combined with powerful permutation-based multiple testing methods, which take into account the dependence among the outcomes.
When nuisance parameters are estimated, the score contributions become correlated and our basic test becomes conservative. To solve this, we consider the effective score. Asymptotically this the part of the score which is uncorrelated with the nuisance scores. The effective score is asymptotically unaffected by the nuisance estimation, so that using it in our method results in an asymptotically exact test. This test is asymptotically equivalent to the parametric score test, if the model is correct. To also obtain near-exactess for very small n in GLMs, we propose a method of orthogonalization of residuals.
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