Differentially Private Kolmogorov-Smirnov-Type Tests. (arXiv:2208.06236v2 [stat.ME] UPDATED)

The test statistics for many nonparametric hypothesis tests can be expressed
in terms of a pseudo-metric applied to the empirical cumulative distribution
function (ecdf), such as Kolmogorov-Smirnov, Kuiper, Cram\'er-von Mises, and
Wasserstein. These test statistics can be used to test goodness-of-fit,
two-samples, paired data, or symmetry. For the design of differentially private
(DP) versions of these tests, we show that test statistics of this form have
small sensitivity, requiring a minimal amount of noise to achieve DP. The tests
are …

tests