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：本文针对存在测量误差的高维线性回归模型，提出了一种用于检验个体假设的创新性检验程序。该方法即使在X模型或Y模型存在误设的情况下仍保持稳健性。我们构建了一个双重稳健的评分函数，该函数在任一模型设定错误时仍保持期望为零，并据此构造了相应的评分检验。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。在高维设定分析中，我们探讨了满足稀疏条件与不满足稀疏条件两种情况，建立了局部备择假设下的渐近正态性与非平凡功效性质。模拟研究与实际数据分析验证了所提方法的有效性。