A unified testing framework is presented for large-dimensional mean vectors of one or several populations which may be non-normal with unequal covariance matrices. Beginning with one-sample case, the construction of tests, underlying assumptions and asymptotic theory, is systematically extended to multi-sample case. Tests are defined in terms of U-statistics-based consistent estimators, and their limits are derived under a few mild assumptions. Accuracy of the tests is shown through simulations. Real data applications, including a five-sample unbalanced MANOVA analysis on count data, are also given.

中文翻译：

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统一的大尺寸均值向量测试方法

提出了一个统一的测试框架，用于一个或几个总体的大型均值向量，这些协方差矩阵可能不正常。从单样本案例开始，测试的构造，基本假设和渐近理论被系统地扩展到多样本案例。测试是根据基于U统计量的一致估计量定义的，其极限是在一些温和的假设下得出的。通过模拟显示测试的准确性。还给出了实际数据应用程序，包括对计数数据的五样本不平衡MANOVA分析。