Confidence intervals are a fundamental tool for quantifying the uncertainty of parameters of interest. With the increase of data privacy awareness, developing a private version of confidence intervals has gained growing attention from both statisticians and computer scientists. Differential privacy is a state-of-the-art framework for analyzing privacy loss when releasing statistics computed from sensitive data. Recent work has been done around differentially private confidence intervals, yet to the best of our knowledge, rigorous methodologies on differentially private confidence intervals in the context of survey sampling have not been studied. In this paper, we propose three differentially private algorithms for constructing confidence intervals for proportions under stratified random sampling. We articulate two variants of differential privacy that make sense for data from stratified sampling designs, analyzing each of our algorithms within one of these two variants. We establish analytical privacy guarantees and asymptotic properties of the estimators. In addition, we conduct simulation studies to evaluate the proposed private confidence intervals, and two applications to the 1940 Census data are provided.

翻译：置信区间是量化目标参数不确定性的基本工具。随着数据隐私意识的增强，开发隐私保护版本的置信区间已引起统计学家和计算机科学家的日益关注。差分隐私是分析从敏感数据计算统计量时隐私损失的前沿框架。近年虽已有关于差分隐私置信区间的研究，但据我们所知，在调查抽样背景下构建差分隐私置信区间的严谨方法论尚未得到系统探索。本文针对分层随机抽样下的比例参数，提出了三种差分隐私算法以构建置信区间。我们阐述了适用于分层抽样数据特征的两种差分隐私变体，并分别在各变体下对每种算法进行分析。我们建立了算法的分析隐私保证及估计量的渐近性质。此外，通过模拟研究评估了所提隐私置信区间的性能，并提供了两个基于1940年人口普查数据的应用实例。