For a high dimensional linear model with a finite number of covariates measured with errors, we study statistical inference on the parameters associated with the error-prone covariates, and propose a new corrected decorrelated score test and a corresponding score type estimator. This work was motivated by a real data example, where both low dimensional phenotypic variables and high dimensional genotypic variables, single nucleotide polymorphisms (SNPs), are available. One of the phenotypic variables is of clinical interest but measured with error. As is standard in the literature, the high dimensional SNPs are assumed to be measured accurately.

We show that the limiting distribution of our corrected decorrelated score test statistic is standard normal under the null hypothesis and retains power under the local alternatives around zero. We also establish the asymptotic normality of the newly proposed estimator, and hence asymptotic confidence intervals can be constructed. The finite-sample performance of the proposed inference procedure is examined through simulation studies. We further illustrate the proposed procedure via an empirical analysis of the real data example mentioned above.

对于具有有限数量的误差测量的协变量的高维线性模型，我们研究了与容易出错的协变量相关的参数的统计推断，并提出了一种新的校正去相关得分测试和相应的得分类型估计器。这项工作是由一个真实的数据示例推动的，在该示例中，低维表型变量和高维基因型变量（单核苷酸多态性（SNP））均可用。表型变量之一具有临床意义，但测量有误。作为文献中的标准，假定高维SNP被精确测量。

我们表明，在零假设下，我们校正的去相关得分测试统计量的极限分布是标准正态分布，在零附近的局部替代项下保留了幂。我们还建立了新提出的估计量的渐近正态性，因此可以构造渐近置信区间。通过仿真研究检查了所提出的推理程序的有限样本性能。我们通过对上述真实数据示例的经验分析进一步说明了所提出的过程。