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：高维回归模型的统计推断因其在基因组学、神经科学和经济学等领域的广泛应用而受到广泛研究。然而，在实际中，常常存在与响应变量和协变量均相关的潜在未测量混杂因素，这可能导致标准去偏方法的失效。本文研究了一个带有隐藏混淆的广义线性回归框架，并提出了一种去偏方法来解决这一高维问题，通过调整未测量混杂因素引起的效应。我们建立了所提出的去偏估计量的一致性和渐近正态性。通过广泛的数值研究及对遗传数据集的应用，验证了所提出方法在有限样本下的性能。