论文标题
关于一般Manova设计中相关矩阵的测试假设
Testing Hypotheses about Correlation Matrices in General MANOVA Designs
论文作者
论文摘要
相关矩阵是研究随机向量或比较它们的依赖性结构的重要工具。我们介绍了一种测试各种无效假设的方法，这些假设可以根据相关矩阵制定。例如，相同相关矩阵的Manova型假设以及对特殊相关结构（例如球形性）的测试。除了现有的第四刻外，我们的方法不需要其他假设，允许在各种设置中进行应用。为了提高样本性能，提出了一种自举技术，理论上是合理的。基于此，我们还提出了一个程序，以同时检验相同相关性和相等协方差矩阵的假设。通过广泛的模拟将所有新测试统计的性能与现有程序进行了比较。
Correlation matrices are an essential tool for investigating the dependency structures of random vectors or comparing them. We introduce an approach for testing a variety of null hypotheses that can be formulated based upon the correlation matrix. Examples cover MANOVA-type hypothesis of equal correlation matrices as well as testing for special correlation structures such as, e.g., sphericity. Apart from existing fourth moments, our approach requires no other assumptions, allowing applications in various settings. To improve the small sample performance, a bootstrap technique is proposed and theoretically justified. Based on this, we also present a procedure to simultaneously test the hypotheses of equal correlation and equal covariance matrices. The performance of all new test statistics is compared with existing procedures through extensive simulations.
