Oliver Dukes (Ghent University).
Title: High-dimensional doubly robust inference for regression parameters:
After variable selection, standard inferential procedures for regression parameters may not be uniformly valid; there is no finite sample size at which a procedure is guaranteed to attain its nominal coverage/size (within pre-specified error margins). This problem is exacerbated in high-dimensional settings, where variable selection becomes unavoidable. This has prompted a flurry of activity in developing uniformly valid confidence intervals and hypothesis tests for a low-dimensional regression parameter (e.g. the effect of a exposure on an outcome) in high-dimensional models. We attempt to unify the recent proposals and obtain inferential procedures that are doubly robust; they are uniformly valid if either a working parametric model for the exposure or the outcome is correctly specified and certain sparsity assumptions hold. When all models are correct, then our confidence intervals will continue to attain their nominal coverage under sparsity conditions weaker than those typically invoked in the literature. The proposal is illustrated in a simulation study and an analysis of routinely collected data obtained from the Ghent University Intensive Care Unit.
