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Confidence intervals are a fundamental tool for quantifying the uncertaintyof parameters of interest. With the increase of data privacy awareness,developing a private version of confidence intervals has gained growingattention from both statisticians and computer scientists. Differential privacyis a state-of-the-art framework for analyzing privacy loss when releasingstatistics computed from sensitive data. Recent work has been done arounddifferentially private confidence intervals, yet to the best of our knowledge,rigorous methodologies on differentially private confidence intervals in thecontext of survey sampling have not been studied. In this paper, we proposethree differentially private algorithms for constructing confidence intervalsfor proportions under stratified random sampling. We articulate two variants ofdifferential privacy that make sense for data from stratified sampling designs,analyzing each of our algorithms within one of these two variants. We establishanalytical privacy guarantees and asymptotic properties of the estimators. Inaddition, we conduct simulation studies to evaluate the proposed privateconfidence intervals, and two applications to the 1940 Census data areprovided.

Differentially Private Confidence Intervals for Proportions under Stratified Random Sampling