Assumption-lean Inference for Generalised Linear Model Parameters

Abstract Inference for the parameters indexing generalised linear models is routinely based on assumption that model correct and a priori specified. This unsatisfactory because chosen usually result of data-adaptive selection process, which may induce excess uncertainty not acknowledged. Moreover, assumptions encoded in rarely represent some known, ground truth, making standard inferences prone to bias, but also failing give pure reflection information contained data. Inspired by developments assumption-free inference so-called projection parameters, we here propose novel nonparametric definitions main effect estimands modification estimands. These reduce when these are correctly specified, have advantage they continue capture respectively (conditional) association between two variables, or degree variables interact their with outcome, even misspecified. We achieve an assumption-lean basis efficient influence function under while invoking flexible (e.g. machine learning) procedures.