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：本文提出在局部差分隐私约束下，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 $(X_1, \dots, X_n)$（均值为 $\mu^\star$）及其隐私化版本 $(Z_1, \dots, Z_n)$，我们仅基于隐私化数据构建了 $\mu^\star$ 的置信区间（CI）和时齐置信序列（CS）。为此，我们引入了Warner著名“随机化应答”机制的非参数、序贯交互推广版本，该版本满足任意有界随机变量的局部差分隐私要求，并基于所得隐私化观测值提供了其均值的置信区间和置信序列。例如，我们的结果在固定时间与时齐框架下均给出了Hoeffding不等式的隐私化对偶形式。进一步，我们将这类Hoeffding型置信序列扩展至时变（非平稳）均值情形，最后通过实例演示如何利用这些方法开展隐私化的在线A/B测试。