This work derives methods for performing nonparametric, nonasymptotic statistical inference for population parameters under the constraint of local differential privacy (LDP). Given observations $(X_1, \dots, X_n)$ with mean $\mu^\star$ that are privatized into $(Z_1, \dots, Z_n)$, we introduce confidence intervals (CI) and time-uniform confidence sequences (CS) for $\mu^\star \in \mathbb R$ when only given access to the privatized data. We introduce a nonparametric and sequentially interactive generalization of Warner's famous "randomized response" mechanism, satisfying LDP for arbitrary bounded random variables, and then provide CIs and CSs for their means given access to the resulting privatized observations. We extend these CSs to capture time-varying (non-stationary) means, and conclude by illustrating how these methods can be used to conduct private online A/B tests.
翻译:这项工作得出了在地方差异隐私的限制下对人口参数进行非参数性、非抽取性统计推断的方法。 根据观测结果,以美元(X_1,\dots,X_n)为单位,以美元($1,\dts, ⁇ n)为单位,用美元净化成美元($1,\dts, ⁇ n)为单位,我们为美元/mu ⁇ star\in\mathbbr R$引入了信任间隔和时间一致的信任序列(CS),但只允许查阅私有化数据。我们引入了Warner著名的“随机响应”机制的非参数性和顺序互动性通用,满足了任意约束随机变量的LDP,然后为CIs和CS提供了获取由此形成的私有化观测手段。我们将这些CS扩展为时间变化(非静止)手段,并通过说明这些方法如何用于进行私人在线A/B测试来结束。