Statistical Approximating Distributions Under Differential Privacy - Yue Wang; Daniel Kifer; Jaewoo Lee; Vishesh Karwa (The Journal of Privacy and Confidentiality, 2018)
Statistics computed from data are viewed as random variables. When they are used for tasks like hypothesis testing and confidence intervals, their true finite sample distributions are often replaced by approximating distributions that are easier to work with (for example, the Gaussian, which results from using approximations justified by the Central Limit Theorem). When data are perturbed by differential privacy, the approximating distributions also need to be modified. Prior work provided various competing methods for creating such approximating distributions with little formal justification beyond the fact that they worked well empirically.