Abstract In this article, we develop new maximum-type tests to infer the overall significance of coefficients in high-dimensional linear models based on the Wilcoxon scores. The proposed testing procedures are free of error variance estimation and robust to heavy-tailed distributions and outliers, making them widely applicable in practice. We incorporate the dependence structure among predictors in the test statistics to enhance their powers. The limiting null distributions of the test statistics are derived to be the extreme value distribution of type I under regularity conditions. To reduce the size distortion, we further propose a multiplier bootstrap method based on the high-dimensional Gaussian approximations, which does not impose any structural assumptions on the unknown covariance matrices. We also evaluate the powers of proposed tests theoretically in comparison with two existing methods. The effectiveness of our proposed tests in the finite samples is illustrated through simulation studies and a real data application.

中文翻译：

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使用 Wilcoxon 分数的高维回归系数的最大类型检验

摘要 在本文中，我们开发了新的最大类型检验，以基于 Wilcoxon 分数推断高维线性模型中系数的整体显着性。所提出的测试程序没有误差方差估计，并且对重尾分布和异常值具有鲁棒性，使其在实践中广泛适用。我们在测试统计中加入了预测变量之间的依赖结构以增强它们的能力。检验统计量的极限零分布被推导出为正则条件下类型 I 的极值分布。为了减少尺寸失真，我们进一步提出了一种基于高维高斯近似的乘法自举方法，该方法不对未知协方差矩阵强加任何结构假设。与两种现有方法相比，我们还从理论上评估了拟议测试的能力。我们提出的有限样本测试的有效性通过模拟研究和实际数据应用得到了说明。