A uniform kernel trick for high-dimensional two-sample problems

Understand

We use a suitable version of the so-called "kernel trick" to devise two-sample (homogeneity) tests, especially focussed on high-dimensional and functional data.

• Our proposal entails a simplification related to the important practical problem of selecting an appropriate kernel function.
• Specifically, we apply a uniform variant of the kernel trick which involves the supremum within a class of kernel-based distances.
• We obtain the asymptotic distribution (under the null and alternative hypotheses) of the test statistic.