Multiple testing has gained much attention in high-dimensional statistical theory and applications, and the problem of variable selection can be regarded as a generalization of the multiple testing. It is aiming to select the important variables among many variables. Performing variable selection in high-dimensional linear models with measurement errors is challenging. Both the influence of high-dimensional parameters and measurement errors need to be considered to avoid severely biases. We consider the problem of variable selection in error-in-variables and introduce the DCoCoLasso-FDP procedure, a new variable selection method. By constructing the consistent estimator of false discovery proportion (FDP) and false discovery rate (FDR), our method can prioritize the important variables and control FDP and FDR at a specifical level in error-in-variables models. An extensive simulation study is conducted to compare DCoCoLasso-FDP procedure with existing methods in various settings, and numerical results are provided to present the efficiency of our method.

多重检验在高维统计理论和应用中备受关注，变量选择问题可以看作是多重检验的推广。它旨在从众多变量中选择重要的变量。在具有测量误差的高维线性模型中执行变量选择具有挑战性。需要同时考虑高维参数和测量误差的影响，以避免严重偏差。我们考虑了变量误差中的变量选择问题，并介绍了 DCoCoLasso-FDP 过程，这是一种新的变量选择方法。通过构造错误发现率（FDP）和错误发现率（FDR）的一致估计量，我们的方法可以优先考虑重要变量，并在变量误差模型中的特定级别控制 FDP 和 FDR。进行了广泛的模拟研究，以在各种设置下比较 DCoCoLasso-FDP 程序与现有方法，并提供数值结果来展示我们方法的效率。