Robust testing in generalized linear models by sign-flipping score contributions

TL;DR

This paper introduces a sign-flipping based semi-parametric test for generalized linear models that is robust to model misspecification and provides improved control of type-I error, even in high-dimensional settings.

Contribution

A novel semi-parametric sign-flipping test for GLMs that handles high-dimensional parameters and accounts for nuisance estimation, improving error control under misspecification.

Findings

Test is robust against overdispersion and heteroscedasticity.

Provides better type-I error control than existing methods.

Asymptotically equivalent to parametric tests when nuisance parameters are estimated.

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 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.