论文标题
有限样品t检验，用于高维平均值
Finite Sample t-Tests for High-Dimensional Means
论文作者
论文摘要
如果需要分化样本量的渐近测试程序，则可能发生尺寸失真，并将样本量较小的数据实现。在本文中，当数据具有高维时，我们考虑平均向量的一样本和两样本测试，但样本量很小。我们建立了一个样本和两样本U统计量的渐近T-分布，仅需要数据维度才能发散，但样本大小要固定，并且不小于3。仿真研究证实了理论上的结果，即提出的测试可以维持多种样本大小和数据维度的准确经验大小。我们将提出的测试应用于fMRI数据集，以证明该方法的实际实现。
Size distortion can occur if an asymptotic testing procedure requiring diverging sample sizes, is implemented to data with very small sample sizes. In this paper, we consider one-sample and two-sample tests for mean vectors when data are high-dimensional but sample sizes are very small. We establish asymptotic t-distributions of one-sample and two-sample U-statistics, which only require data dimensionality to diverge but sample sizes to be fixed and no less than 3. Simulation studies confirm the theoretical results that the proposed tests maintain accurate empirical sizes for a wide range of sample sizes and data dimensionalities. We apply the proposed tests to an fMRI dataset to demonstrate the practical implementation of the methods.
