In this work, we introduce a new approach for statistical quantification of differential privacy in a black box setting. We present estimators and confidence intervals for the optimal privacy parameter of a randomized algorithm A, as well as other key variables (such as the “data-centric privacy level”). Our estimators are based on a local characterization of privacy and in contrast to the related literature avoid the process of “event selection” - a major obstacle to privacy validation. This makes our methods easy to implement and user-friendly. We show fast convergence rates of the estimators and asymptotic validity of the confidence intervals. An experimental study of various algorithms confirms the efficacy of our approach.