  Statistical inferences for high-dimensional regression models have been
extensively studied for their wide applications ranging from genomics,
neuroscience, to economics. However, in practice, there are often potential
unmeasured confounders associated with both the response and covariates, which
can lead to invalidity of standard debiasing methods. This paper focuses on a
generalized linear regression framework with hidden confounding and proposes a
debiasing approach to address this high-dimensional problem, by adjusting for
the effects induced by the unmeasured confounders. We establish consistency and
asymptotic normality for the proposed debiased estimator. The finite sample
performance of the proposed method is demonstrated through extensive numerical
studies and an application to a genetic data set.
