  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.
