Abstract

For multi-sample covariance testing, the classical likelihood ratio test is often efficient and powerful in low-dimensional normal cases. However, when the dimension is larger than the sample size, it fails to work in practice and theory. This paper proposes a permutation based test to handle high-dimensional covariance testing problem with more than two samples. Numerical studies show that the test controls type I error rate well for both normal and non-normal data. The power performance is also competitive with existing methods. In addition, a real data example of DNA microarray is analyzed for illustration.

中文翻译：

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基于置换的多样本高维协方差矩阵检验新方法

摘要

对于多样本协方差检验，经典似然比检验在低维正常情况下通常是有效且强大的。但是，当维度大于样本量时，它在实践和理论上都行不通。本文提出了一种基于置换的测试来处理具有两个以上样本的高维协方差测试问题。数值研究表明，对于正态和非正态数据，该检验都能很好地控制 I 类错误率。功率性能也与现有方法具有竞争力。此外，还分析了 DNA 微阵列的真实数据示例以进行说明。