  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.
