# Differentially Private Nonparametric Confidence Intervals Under Minimal Distributional Assumptions

arXiv: https://arxiv.org/abs/2511.01303 · HTML: https://mlsanity.com/paper/2511.01303/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 41 references that are in the map.
- First posted on arXiv 3 Nov 2025.

## Builds on (most cited first, 19 of 19)

- [Privacy Amplification by Subsampling: Tight Analyses via Couplings and Divergences](https://mlsanity.com/paper/1807.01647/) (2018)
- [Finite Sample Differentially Private Confidence Intervals](https://mlsanity.com/paper/1711.03908/) (2017)
- [Revisiting differentially private linear regression: optimal and adaptive prediction & estimation in unbounded domain](https://mlsanity.com/paper/1803.02596/) (2018)
- [The Noisy Power Method: A Meta Algorithm with Applications](https://mlsanity.com/paper/1311.2495/) (2013)
- [Average-Case Averages: Private Algorithms for Smooth Sensitivity and Mean Estimation](https://mlsanity.com/paper/1906.02830/) (2019)
- [Differentially Private Quantiles](https://mlsanity.com/paper/2102.08244/) (2021)
- [Differentially Private Confidence Intervals](https://mlsanity.com/paper/2001.02285/) (2020)
- [Unbiased Statistical Estimation and Valid Confidence Intervals Under Differential Privacy](https://mlsanity.com/paper/2110.14465/) (2021)
- [Differentially Private Covariance Revisited](https://mlsanity.com/paper/2205.14324/) (2022)
- [Differentially Private Approximate Quantiles](https://mlsanity.com/paper/2110.05429/) (2021)
- [Differentially Private Confidence Intervals for Empirical Risk Minimization](https://mlsanity.com/paper/1804.03794/) (2018)
- [Differentially Private Bootstrap: New Privacy Analysis and Inference Strategies](https://mlsanity.com/paper/2210.06140/) (2022)
- [Non-parametric Differentially Private Confidence Intervals for the Median](https://mlsanity.com/paper/2106.10333/) (2021)
- [Identification, Amplification and Measurement: A bridge to Gaussian Differential Privacy](https://mlsanity.com/paper/2210.09269/) (2022)
- [Unbounded Differentially Private Quantile and Maximum Estimation](https://mlsanity.com/paper/2305.01177/) (2023)
- [Resampling methods for private statistical inference](https://mlsanity.com/paper/2402.07131/) (2024)
- [Differentially Private Kolmogorov-Smirnov-Type Tests](https://mlsanity.com/paper/2208.06236/) (2022)
- [Gaussian Differential Private Bootstrap by Subsampling](https://mlsanity.com/paper/2505.01197/) (2025)
- [Differentially private ratio statistics](https://mlsanity.com/paper/2505.20351/) (2025)

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

- [One-Shot Private Confidence Regions via Resampling](https://mlsanity.com/paper/2610.08460/) (2026)

## Abstract (arXiv)

We consider the problem of constructing differentially private nonparametric confidence intervals (CIs) for an arbitrary quantity using resampling. A growing body of work has adapted resampling ideas to the private setting, including private bootstrap methods citebrawner2018bootstrap, wang2025differentially,dette2025gaussian and BLB-based subsample-and-aggregate approaches citecovington2025unbiased, chadha2024resampling. However, existing methods typically rely on strong assumptions, such as asymptotic normality, or are tied to specific privacy mechanisms such as noise addition, and can be impractical in finite-sample regimes. We address these problems by introducing a simple, general framework that can convert any differentially private estimator satisfying mild conditions into a differentially private nonparametric CI for arbitrary target quantities. Our method repeatedly subsamples the data, applies the private estimator to each subset, and post-processes the resulting empirical CDF into a CI. The framework is black-box, and does not require a specific limiting distribution. We prove that the empirical CDF induced by our procedure converges to the sampling distribution of the private statistic, which implies that the resulting CI is asymptotically valid and tight, and provide heuristic guidance for choosing the hyperparameters. Empirically, our method outperforms competing general approaches, especially for non-smooth functionals and more challenging distributions.