Recent results for comparison of high-dimensional mean vectors make assumptions that require weak dependence between the variables. These requirements fail to be satisfied, for example, by elliptically contoured distributions. In this paper, we relax the dependence conditions that seem to be the standard assumption in high-dimensional asymptotics. With the relaxed condition, the scope of applicability of the results broadens. In particular, an α-mixing type of dependence and general conditions on the variance of quadratic forms are covered. The problem is set up in a general and flexible form that extension of the results to general factorial design and profile analysis are formally illustrated. Simulation studies are used to evaluate the numerical performance of the results in practical scenarios. Data from an Electroencephalograph (EEG) experiment is analysed as an illustrative example.

用于比较高维平均向量的最新结果做出了需要变量之间弱相关性的假设。例如，椭圆轮廓分布无法满足这些要求。在本文中，我们放宽了似乎是高维渐近学中标准假设的依赖条件。随着条件的放松，结果的适用范围扩大了。特别地，α- 涵盖了二次形式方差的混合依赖类型和一般条件。该问题以通用且灵活的形式设置，正式说明了将结果扩展到通用因子设计和剖面分析。模拟研究用于评估结果在实际场景中的数值性能。来自脑电图 (EEG) 实验的数据作为说明性示例进行分析。