Differentially private scale testing via rank transformations and percentile modifications
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866918083559424000 |
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| author | Levine, Joshua Ramsay, Kelly |
| author_facet | Levine, Joshua Ramsay, Kelly |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_03725 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Differentially private scale testing via rank transformations and percentile modifications Levine, Joshua Ramsay, Kelly Methodology Machine Learning 62G10, 62G20, 62G30, 68P27 G.3.1; G.3.5; K.6.5 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. |
| title | Differentially private scale testing via rank transformations and percentile modifications |
| topic | Methodology Machine Learning 62G10, 62G20, 62G30, 68P27 G.3.1; G.3.5; K.6.5 |
| url | https://arxiv.org/abs/2507.03725 |