The Wilcoxon signed-rank test and the Wilcoxon-Mann-Whitney test are commonly employed in one sample and two sample mean tests for one-dimensional hypothesis problems. For high-dimensional mean test problems, we calculate the asymptotic distribution of the maximum of rank statistics for each variable and suggest a max-type test. This max-type test is then merged with a sum-type test, based on their asymptotic independence offered by stationary and strong mixing assumptions. Our numerical studies reveal that this combined test demonstrates robustness and superiority over other methods, especially for heavy-tailed distributions.

翻译：Wilcoxon符号秩检验和Wilcoxon-Mann-Whitney检验常用于一维假设问题中的单样本和双样本均值检验。针对高维均值检验问题，我们计算了每个变量秩统计量最大值的渐近分布，并提出了一种最大值型检验。基于平稳性和强混合假设下这两类检验的渐近独立性，我们将该最大值型检验与总和型检验进行融合。数值研究表明，这种组合检验方法表现出稳健性，且在重尾分布场景下优于其他方法。