广义核双样本检验
Generalized Kernel Two-Sample Tests
AI总结：
提出一种利用中高维共性模式的广义核双样本检验统计量，显著提升效能并降低计算成本，在R包kerTests中实现，应用于分子形状与出租车行程比较。
摘要：
核双样本检验已被广泛用于多元数据以检验分布是否相等。然而，现有基于将分布映射到再生核希尔伯特空间的方法主要针对特定备择假设，并且在数据维度中等至较高时，由于维数灾难，在某些场景下表现不佳。我们提出了一种新的检验统计量，利用中等和高维度下的常见模式，在广泛的备择假设下比现有核双样本检验实现了显著的效能提升。我们还提出了替代的检验程序，在保持高效能的同时降低计算成本，为大数据集提供了易于使用的现成工具。新方法在各种设置下与其他最先进的检验进行了比较，表现出良好的性能。我们通过两个应用展示了新方法：利用分子形状比较麝香与非麝香，以及比较连续月份从约翰·肯尼迪机场出发的出租车行程。所有提出的方法均在R包kerTests中实现。
英文摘要：
Kernel two-sample tests have been widely used for multivariate data to test equality of distributions. However, existing tests based on mapping distributions into a reproducing kernel Hilbert space mainly target specific alternatives and do not work well for some scenarios when the dimension of the data is moderate to high due to the curse of dimensionality. We propose a new test statistic that makes use of a common pattern under moderate and high dimensions and achieves substantial power improvements over existing kernel two-sample tests for a wide range of alternatives. We also propose alternative testing procedures that maintain high power with low computational cost, offering easy off-the-shelf tools for large datasets. The new approaches are compared to other state-of-the-art tests under various settings and show good performance. We showcase the new approaches through two applications: The comparison of musks and non-musks using the shape of molecules, and the comparison of taxi trips starting from John F. Kennedy airport in consecutive months. All proposed methods are implemented in an R package kerTests.
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