标题： 使用R包CovCorTest检验协方差和相关矩阵的假设 显示英文标题

标题： Testing Hypotheses regarding Covariance and Correlation matrices with the R package CovCorTest

摘要： 除了常用的定位度量外，方差和相关性等离散度度量也提供了许多有价值的信息。 因此，它们在多元统计中起着至关重要的作用，这导致了关于协方差和相关矩阵的检验。 此外，这些矩阵的结构也导致了重要的研究假设，因为它们包含了关于基础模型的重要信息。 事实上，关于协方差和相关矩阵结构的假设在统计建模和检验中往往是基本的。 在此背景下，具有最少分布假设和非常一般假设的半参数设置对于实现广泛的应用是必不可少的。 免费提供的包CovCorTest提供了针对上述所有问题的适当检验，使用引导法和其他类似技术以实现良好的性能，尤其是在小样本情况下。 此外，该包为两个中心检验中正在研究的假设提供了灵活的规范选项，能够满足不同专业水平的用户，从而同时实现了高度的灵活性和用户友好性。 本文还介绍了\textbf{协方差相关性检验}在各种问题中的应用，通过多个示例进行说明，其中测试被应用于一个现实世界的数据集。 显示英文摘要

摘要： In addition to the commonly analyzed measures of location, dispersion measurements such as variance and correlation provide many valuable information. Consequently, they play a crucial role in multivariate statistics, which leads to tests regarding covariance and correlation matrices. Furthermore, also the structure of these matrices leads to important hypotheses of interest, since it contains substantial information about the underlying model. In fact, assumptions regarding the structures of covariance and correlation matrices are often fundamental in statistical modelling and testing. In this context, semi-parametric settings with minimal distributional assumptions and very general hypotheses are essential for enabling manifold usage. The free available package CovCorTest provides suitable tests addressing all aforementioned issues, using bootstrap and similar techniques to achieve good performance, particularly in small samples. Additionally, the package offers flexible specification options for the hypotheses under investigation in two central tests, accommodating users with varying levels of expertise, which results in high flexibility and user-friendliness at the same time. This paper also presents the application of \textbf{CovCorTest} for various issues, illustrated by multiple examples, where the tests are applied to a real-world dataset.