This work derives methods for performing nonparametric, nonasymptotic statistical inference for population means under the constraint of local differential privacy (LDP). Given bounded observations $(X_1, \dots, X_n)$ with mean $\mu^\star$ that are privatized into $(Z_1, \dots, Z_n)$, we present confidence intervals (CI) and time-uniform confidence sequences (CS) for $\mu^\star$ when only given access to the privatized data. To achieve this, 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. For example, our results yield private analogues of Hoeffding's inequality in both fixed-time and time-uniform regimes. We extend these Hoeffding-type 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：这项工作产生一些方法,用于在当地差异隐私的限制下对人口手段进行非参数性、非抽取性统计推断。根据约束性观察,以美元(X_1,\dots,X_n)为单位,以美元为单位,以美元(%1,\dts, ⁇ n)为单位私有化,我们为只允许查阅私有化数据时的美元提供置信间隔(CI)和时间统一信任序列(CS)。为了实现这一点,我们引入了对沃纳著名的“随机响应”机制的非参数性和顺序性互动的概括化,满足任意约束性随机变量的LDP,然后向CIs和CS提供其手段,使其获得由此产生的私有化观察。例如,我们的结果在固定时间和时间统一制度下产生了Hoffding的不平等的私人类比。我们将这些Hoffding-s型CSs推广到捕捉取时间分配(非固定)手段,结论是说明这些方法如何用于进行私人在线A/B测试。