On the High Dimensional Power of a Linear-Time Two Sample Test under Mean-shift Alternatives

Nonparametric two sample testing deals with the question of consistently deciding if two distributions are dierent, given samples from both, without making any parametric assumptions about the form of the distributions. The current literature is split into two kinds of tests - those which are consistent without any assumptions about how the distributions may dier ( general alternatives), and those which are designed to specically test easier alternatives, like a dierence in

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