Nonparametric Tests between Distributions

Reproducing Kernel Hilbert Spaces have been mainly used for estimation. Distributional tests in this area were mainly concerned with tests for independence of random variables. We give concentration of measure bounds for the latter using an easy to compute criterion between spaces of observations. In addition, we show that a similar criterion can be used easily for the purpose of testing the identity between two distributions. In both cases, we prove necessary and sufficient conditions for the tests.