We investigate differentially private estimators for individual parameters within larger parametric models. While generic private estimators exist, the estimators we provide repose on new local notions of estimand stability, and these notions allow procedures that provide private certificates of their own stability. By leveraging these private certificates, we provide computationally and statistical efficient mechanisms that release private statistics that are, at least asymptotically in the sample size, essentially unimprovable: they achieve instance optimal bounds. Additionally, we investigate the practicality of the algorithms both in simulated data and in real-world data from the American Community Survey and US Census, highlighting scenarios in which the new procedures are successful and identifying areas for future work.

翻译：我们研究了大型参数模型中单个参数的差分隐私估计器。尽管存在通用的隐私估计器，但我们提出的估计器基于新的估计量稳定性局部概念，这些概念允许程序提供其自身稳定性的隐私证明。通过利用这些隐私证明，我们提供了计算和统计效率高的机制，这些机制发布的隐私统计量至少在样本量渐近意义上基本无法改进：它们达到了实例最优界。此外，我们在模拟数据和美国社区调查及美国人口普查的真实数据中验证了算法的实用性，重点展示了新方法成功的应用场景，并指出了未来工作的改进方向。