# Resampling methods for private statistical inference

arXiv: https://arxiv.org/abs/2402.07131 · HTML: https://mlsanity.com/paper/2402.07131/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 42 references that are in the map.
- First posted on arXiv 11 Feb 2024.

## Builds on (most cited first, 15 of 15)

- [Retiring Adult: New Datasets for Fair Machine Learning](https://mlsanity.com/paper/2108.04884/) (2021)
- [Finite Sample Differentially Private Confidence Intervals](https://mlsanity.com/paper/1711.03908/) (2017)
- [CoinPress: Practical Private Mean and Covariance Estimation](https://mlsanity.com/paper/2006.06618/) (2020)
- [Asymptotic Optimality in Stochastic Optimization](https://mlsanity.com/paper/1612.05612/) (2016)
- [Differentially Private Ordinary Least Squares](https://mlsanity.com/paper/1507.02482/) (2015)
- [Differentially Private Simple Linear Regression](https://mlsanity.com/paper/2007.05157/) (2020)
- [Differentially private inference via noisy optimization](https://mlsanity.com/paper/2103.11003/) (2021)
- [Near Instance-Optimality in Differential Privacy](https://mlsanity.com/paper/2005.10630/) (2020)
- [Parametric Bootstrap for Differentially Private Confidence Intervals](https://mlsanity.com/paper/2006.07749/) (2020)
- [Confidence-Ranked Reconstruction of Census Microdata from Published Statistics](https://mlsanity.com/paper/2211.03128/) (2022)
- [Locally Private Mean Estimation: Z-test and Tight Confidence Intervals](https://mlsanity.com/paper/1810.08054/) (2018)
- [Unbiased Statistical Estimation and Valid Confidence Intervals Under Differential Privacy](https://mlsanity.com/paper/2110.14465/) (2021)
- [Differentially Private Confidence Intervals for Empirical Risk Minimization](https://mlsanity.com/paper/1804.03794/) (2018)
- [Non-parametric Differentially Private Confidence Intervals for the Median](https://mlsanity.com/paper/2106.10333/) (2021)
- [Hypothesis Testing for Differentially Private Linear Regression](https://mlsanity.com/paper/2206.14449/) (2022)

## Built on by (most cited first, 4 of 4)

- [Gaussian Differential Private Bootstrap by Subsampling](https://mlsanity.com/paper/2505.01197/) (2025)
- [Differentially Private Nonparametric Confidence Intervals Under Minimal Distributional Assumptions](https://mlsanity.com/paper/2511.01303/) (2025)
- [Privately Estimating Monotone Statistics in Polynomial Time](https://mlsanity.com/paper/2605.27912/) (2026)
- [One-Shot Private Confidence Regions via Resampling](https://mlsanity.com/paper/2610.08460/) (2026)

## Abstract (arXiv)

We consider the task of constructing confidence intervals with differential privacy. We propose two private variants of the non-parametric bootstrap, which privately compute the median of the results of multiple "little" bootstraps run on partitions of the data and give asymptotic bounds on the coverage error of the resulting confidence intervals. For a fixed differential privacy parameter ε, our methods enjoy the same error rates as that of the non-private bootstrap to within logarithmic factors in the sample size n. We empirically validate the performance of our methods for mean estimation, median estimation, and logistic regression with both real and synthetic data. Our methods achieve similar coverage accuracy to existing methods (and non-private baselines) while providing notably shorter (gtrsim 10 times) confidence intervals than previous approaches.