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:摘要:高维回归模型的统计推断在基因组学、神经科学和经济学等广泛的应用中得到了广泛研究。然而,在实践中,响应和协变量通常存在潜在的未测量的交互作用,这可能导致标准去偏方法的无效性。本文针对具有隐藏交互作用的广义线性回归框架提出了一种去偏方法,通过调整由未测量的交互作用引起的效应来解决这一高维问题。我们证明了所提出的去偏估计器的一致性和渐近正态性。通过大量的数值研究和一个基因数据集的应用,展示了所提出方法的有限样本性能。