In this paper, the problem of high-dimensional multivariate analysis of variance is investigated under a low-dimensional factor structure which violates some vital assumptions on covariance matrix in some existing literature. We propose a new test and derive that the asymptotic distribution of the test statistic is a weighted distribution of chi-squares of 1 degree of freedom under the null hypothesis and mild conditions. We provide numerical studies on both sizes and powers to illustrate performance of the proposed test.

中文翻译：

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低维因子结构下方差多变量分析的高维检验

在本文中，研究了在违反现有文献中协方差矩阵的一些重要假设的低维因子结构下的高维多元方差分析问题。我们提出了一个新的检验，并推导出检验统计量的渐近分布是零假设和温和条件下 1 自由度卡方的加权分布。我们提供了关于大小和功率的数值研究，以说明所提议测试的性能。