The paper focuses on developing differentially private confidence intervals for population proportions under stratified random sampling. It presents three algorithms that add noise at different levels (stratum or population) to achieve differential privacy, depending on whether the sample sizes are public or private.
The key highlights and insights are:
The authors articulate two variants of differential privacy that are appropriate for data from stratified sampling designs: "substitute-one relation within a stratum" and "remove/add-one relation".
The proposed algorithms propagate the uncertainty due to the application of differentially private mechanisms into the construction of confidence intervals, with necessary bias corrections to achieve asymptotic unbiased variance estimates.
Theoretical results are provided to guarantee the desired privacy level and asymptotic coverage properties of the confidence intervals under each algorithm.
The authors analyze and compare the additional variance introduced by the noise addition across the three algorithms, relating it to the sampling weights.
Simulation studies and two applications to the 1940 Census data are conducted to evaluate the performance of the proposed private confidence intervals.
Overall, the paper establishes the first rigorous methodologies on differentially private confidence intervals in the context of survey sampling, which is an important area in statistics.
To Another Language
from source content
arxiv.org
Дополнительные вопросы