# On Privately Estimating a Single Parameter

arXiv: https://arxiv.org/abs/2503.17252 · HTML: https://mlsanity.com/paper/2503.17252/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Mar 2025.

## Built on by (most cited first, 1 of 1)

- [Privately Estimating Monotone Statistics in Polynomial Time](https://mlsanity.com/paper/2605.27912/) (2026)

## Abstract (arXiv)

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.