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This work derives methods for performing nonparametric, nonasymptoticstatistical inference for population means under the constraint of localdifferential privacy (LDP). Given bounded observations $(X_1, \dots, X_n)$ withmean $\mu^\star$ that are privatized into $(Z_1, \dots, Z_n)$, we presentconfidence intervals (CI) and time-uniform confidence sequences (CS) for$\mu^\star$ when only given access to the privatized data. To achieve this, weintroduce a nonparametric and sequentially interactive generalization ofWarner's famous ``randomized response'' mechanism, satisfying LDP for arbitrarybounded random variables, and then provide CIs and CSs for their means givenaccess to the resulting privatized observations. For example, our results yieldprivate analogues of Hoeffding's inequality in both fixed-time and time-uniformregimes. We extend these Hoeffding-type CSs to capture time-varying(non-stationary) means, and conclude by illustrating how these methods can beused to conduct private online A/B tests.

Nonparametric extensions of randomized response for private confidence sets