On Privately Estimating a Single Parameter
This work addresses privacy concerns in statistical estimation for applications like census data, though it appears incremental by building on existing private estimators with new stability concepts.
The paper tackles the problem of differentially private estimation of individual parameters within larger models by introducing new local notions of estimand stability, resulting in mechanisms that achieve instance optimal bounds and are computationally and statistically efficient, with practical validation on simulated and real-world data.
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.