We develop a near-optimal testing procedure under the framework of Gaussian differential privacy for simple as well as one- and two-sided tests under monotone likelihood ratio conditions. Our mechanism is based on a private mean estimator with data-driven clamping bounds, whose population risk matches the private minimax rate up to logarithmic factors. Using this estimator, we construct private test statistics that achieve the same asymptotic relative efficiency as the non-private, most powerful tests while maintaining conservative type I error control. In addition to our theoretical results, our numerical experiments show that our private tests outperform competing DP methods and offer comparable power to the non-private most powerful tests, even at moderately small sample sizes and privacy loss budgets.

翻译：我们针对简单假设以及单调似然比条件下的单侧与双侧检验，在高斯差分隐私框架下开发了一种近乎最优的检验方法。该机制基于一种采用数据驱动截断界的私有均值估计器，其总体风险与私有极小极大率在至多对数因子范围内相匹配。利用该估计器，我们构建了私有检验统计量，在保持保守的第一类错误控制的同时，实现了与非私有最有效检验相同的渐近相对效率。除理论结果外，数值实验表明，即使在样本量中等偏小且隐私损失预算有限的情况下，我们的私有检验方法也优于其他差分隐私方法，并提供了与非私有最有效检验相当的检验功效。