Finite sample t-tests for high-dimensional means
Finite sample t-tests for high-dimensional means
复制标题
DOI：
10.1016/j.jmva.2023.105183
复制
发表时间：
2022-03
影响因子：
1.6
通讯作者：
Jun Li
中科院分区：
文献类型：
--
作者：
Jun Li
当样本量较小时，需要分散样本量以保持准确的I型错误率的渐近检验变得具有挑战性。在本文中，当数据是高维的，但样本容量非常小时，我们考虑了均值向量的单样本、双样本和方差分析检验。我们建立了所提出的u统计量的渐近t分布，它只要求数据维数发散，但样本量固定且不小于3。拟议的测试在广泛的样本量和数据维度范围内保持准确的第一类错误率。此外，检验是非参数的，可以应用于正态分布或重尾数据。仿真研究证实了试验的理论结果。我们还将提出的测试应用于fMRI数据集，以演示该方法的实际实施。
When sample sizes are small, it becomes challenging for an asymptotic test requiring diverging sample sizes to maintain an accurate Type I error rate. In this paper, we consider one-sample, two-sample and ANOVA tests for mean vectors when data are high-dimensional but sample sizes are very small. We establish asymptotic t-distributions of the proposed U-statistics, which only require data dimensionality to diverge but sample sizes to be fixed and no less than 3. The proposed tests maintain accurate Type I error rates for a wide range of sample sizes and data dimensionality. Moreover, the tests are nonparametric and can be applied to data which are normally distributed or heavy-tailed. Simulation studies confirm the theoretical results for the tests. We also apply the proposed tests to an fMRI dataset to demonstrate the practical implementation of the methods.