{"ID":2898473,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2507.03725","arxiv_id":"2507.03725","title":"Differentially private scale testing via rank transformations and percentile modifications","abstract":"We develop a class of differentially private two-sample scale tests, called the rank-transformed percentile-modified Siegel--Tukey tests, or RPST tests. These RPST tests are inspired both by recent differentially private extensions of some common rank tests and some older modifications to non-private rank tests. We present the asymptotic distribution of the RPST test statistic under the null hypothesis, under a very general condition on the rank transformation. We also prove RPST tests are differentially private, and that their type I error does not exceed the given level. We uncover that the growth rate of the rank transformation presents a tradeoff between power and sensitivity. We do extensive simulations to investigate the effects of the tuning parameters and compare to a general private testing framework. Lastly, we show that our techniques can also be used to improve the differentially private signed-rank test.","short_abstract":"We develop a class of differentially private two-sample scale tests, called the rank-transformed percentile-modified Siegel--Tukey tests, or RPST tests. These RPST tests are inspired both by recent differentially private extensions of some common rank tests and some older modifications to non-private rank tests. We pre...","url_abs":"https://arxiv.org/abs/2507.03725","url_pdf":"https://arxiv.org/pdf/2507.03725v1","authors":"[\"Joshua Levine\",\"Kelly Ramsay\"]","published":"2025-07-04T17:25:50Z","proceeding":"stat.ME","tasks":"[\"stat.ME\",\"cs.LG\"]","methods":"[]","has_code":false}