提出新型差分隐私两样本尺度检验方法，兼顾统计功效与隐私保护。
Differentially private scale testing via rank transformations and percentile modifications
- 基于秩变换与百分位修正构造隐私保护检验
- 理论证明其在任意秩变换下均满足差分隐私且犯Ⅰ类错误率可控
- 适用于需要严格隐私保护的统计推断场景
我们提出一类新的差分隐私两样本尺度检验方法，称为秩变换百分位修正的Siegel-Tukey检验（RPST）。该方法受近期差分隐私秩检验扩展及旧版非隐私秩检验修正的启发。在对秩变换施加非常一般性条件下，给出了RPST检验统计量在零假设下的渐近分布。证明了RPST检验具有差分隐私性，且第一类错误率不超过设定水平。揭示了秩变换增长速率在检验功效与敏感度之间存在权衡。通过大量模拟研究调参影响，并与通用私有检验框架对比。最后表明，该技术也可用于改进差分隐私符号秩检验。
原文摘要 · Abstract (English)
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.
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