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.

翻译：针对高维回归模型的统计推断因其在基因组学、神经科学及经济学等领域的广泛应用而得到深入研究。然而，在实际应用中，通常存在与响应变量及协变量均相关的未测量潜在混杂因素，这可能导致标准去偏方法失效。本文聚焦于存在隐藏混杂的广义线性回归框架，通过校正未测量混杂因素引发的效应，提出一种解决该高维问题的去偏方法。我们建立了所提去偏估计量的一致性和渐近正态性。通过大量数值实验及遗传数据集的实际应用，验证了该方法在有限样本下的性能。