Equivalence of distance-based and RKHS-based statistics in hypothesis testing

How two ways of testing data are actually the same — and why it matters

Imagine two tools people use to check if two groups are different or if two things are linked.
One comes from older stats ideas called energy distance, the other from machine learning known as MMD.
It turns out they can be two faces of the same thing, when you pick the right kernel.
That means a test made one way can be seen in the other language, so methods cross over easy, and you get new options.
Some choices of kernel match the usual energy method, but other choices can make tests more powerful, catching subtle differences that were missed before.
This opens way to swap ideas, try new kernels and tune tests for real data, without learning a whole new toolbox.
It also shows when these tests will always find a difference if one exists, and when they might fail.
For anyone checking data — scientists, students, curious people — this link makes testing clearer and gives simple tricks to improve results, so your conclusions are stronger and more reliable.

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Equivalence of distance-based and RKHS-based statistics in hypothesis testing

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