In this paper, we introduce an innovative testing procedure for assessing individual hypotheses in high-dimensional linear regression models with measurement errors. This method remains robust even when either the X-model or Y-model is misspecified. We develop a double robust score function that maintains a zero expectation if one of the models is incorrect, and we construct a corresponding score test. We first show the asymptotic normality of our approach in a low-dimensional setting, and then extend it to the high-dimensional models. Our analysis of high-dimensional settings explores scenarios both with and without the sparsity condition, establishing asymptotic normality and non-trivial power performance under local alternatives. Simulation studies and real data analysis demonstrate the effectiveness of the proposed method.

翻译：本文提出了一种创新的检验方法，用于评估存在测量误差的高维线性回归模型中的个体假设。即使X模型或Y模型存在误设，该方法仍保持稳健性。我们构建了一个双重稳健的得分函数，当其中一个模型设定错误时，该函数仍保持期望为零，并据此构造了相应的得分检验。我们首先在低维设定下证明了该方法的渐近正态性，随后将其推广至高维模型。针对高维场景，我们分别探讨了满足与不满足稀疏性条件的情况，建立了局部备择假设下的渐近正态性与非平凡功效性能。模拟研究与实际数据分析验证了所提方法的有效性。