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：本文研究了在局部差分隐私（LDP）约束下，针对总体均值进行非参数、非渐近统计推断的方法。给定有界观测值 $(X_1, \dots, X_n)$（其均值为 $\mu^\star$）经隐私化处理后得到 $(Z_1, \dots, Z_n)$，本文在仅能访问私有化数据的情况下，提出了关于 $\mu^\star$ 的置信区间（CI）和时一致置信序列（CS）。为实现这一目标，我们引入了一种非参数且可顺序交互的推广形式——即华纳著名的“随机响应”机制，该机制满足任意有界随机变量的LDP约束，并基于由此得到的私有化观测值，提供了其均值的CI和CS。例如，我们的结果在固定时间与时一致两种框架下均给出了Hoeffding不等式的隐私化版本。进一步地，我们将这些Hoeffding型CS扩展至捕捉时变（非平稳）均值，最后通过实例说明如何利用这些方法开展隐私化的在线A/B测试。