论文标题
高维协方差矩阵的两样本测试：一种正常参考方法
Two-Sample Test for High-Dimensional Covariance Matrices: a normal-reference approach
论文作者
论文摘要
测试两个高维样品的协方差矩阵的平等性是统计中的基本推论问题。已经提出了一些测试，但是当不满足所需的假设时，它们要么太自由或过于保守，因此证明它们并不总是适用于实际数据分析。为了克服这一困难，在本文中提出和研究了正常的参考测试。结果表明，在某些规律性条件和零假设下，提出的测试统计量和卡方型混合物具有相同的限制分布。然后，使用卡方型混合物的测试统计量近似于拟议的测试统计量的无效分布。可以使用三个肿瘤匹配的卡方应用及其近似参数始终从数据中估算的近似参数，可以很好地估算卡方型混合物的分布。还建立了在当地替代方案下提出的测试的渐近能力。仿真研究和一个真实数据示例表明，在大小控制方面，提出的测试的表现大大优于现有竞争对手。
Testing the equality of the covariance matrices of two high-dimensional samples is a fundamental inference problem in statistics. Several tests have been proposed but they are either too liberal or too conservative when the required assumptions are not satisfied which attests that they are not always applicable in real data analysis. To overcome this difficulty, a normal-reference test is proposed and studied in this paper. It is shown that under some regularity conditions and the null hypothesis, the proposed test statistic and a chi-square-type mixture have the same limiting distribution. It is then justified to approximate the null distribution of the proposed test statistic using that of the chi-square-type mixture. The distribution of the chi-square-type mixture can be well approximated using a three-cumulant matched chi-square-approximation with its approximation parameters consistently estimated from the data. The asymptotic power of the proposed test under a local alternative is also established. Simulation studies and a real data example demonstrate that in terms of size control, the proposed test outperforms the existing competitors substantially.
