# Parametric Bootstrap for Differentially Private Confidence Intervals

arXiv: https://arxiv.org/abs/2006.07749 · HTML: https://mlsanity.com/paper/2006.07749/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Jun 2020.

## Built on by (most cited first, 19 of 19)

- [A Bias-Accuracy-Privacy Trilemma for Statistical Estimation](https://mlsanity.com/paper/2301.13334/) (2023)
- [Private Gradient Descent for Linear Regression: Tighter Error Bounds and Instance-Specific Uncertainty Estimation](https://mlsanity.com/paper/2402.13531/) (2024)
- [Differentially Private Bootstrap: New Privacy Analysis and Inference Strategies](https://mlsanity.com/paper/2210.06140/) (2022)
- [Noise-Aware Statistical Inference with Differentially Private Synthetic Data](https://mlsanity.com/paper/2205.14485/) (2022)
- [Nonparametric extensions of randomized response for private confidence sets](https://mlsanity.com/paper/2202.08728/) (2022)
- [Training Private Models That Know What They Don't Know](https://mlsanity.com/paper/2305.18393/) (2023)
- [Differentially Private Covariate Balancing Causal Inference](https://mlsanity.com/paper/2410.14789/) (2024)
- [Resampling methods for private statistical inference](https://mlsanity.com/paper/2402.07131/) (2024)
- [Does Differentially Private Synthetic Data Lead to Synthetic Discoveries?](https://mlsanity.com/paper/2403.13612/) (2024)
- [Private Regression via Data-Dependent Sufficient Statistic Perturbation](https://mlsanity.com/paper/2405.15002/) (2024)
- [PrivATE: Differentially Private Confidence Intervals for Average Treatment Effects](https://mlsanity.com/paper/2505.21641/) (2025)
- [Recycling Scraps: Improving Private Learning by Leveraging Intermediate Checkpoints](https://mlsanity.com/paper/2210.01864/) (2022)
- [Differentially Private Distributed Bayesian Linear Regression with MCMC](https://mlsanity.com/paper/2301.13778/) (2023)
- [Uncertainty quantification by block bootstrap for differentially private stochastic gradient descent](https://mlsanity.com/paper/2405.12553/) (2024)
- [Fiducial Matching: Differentially Private Inference for Categorical Data](https://mlsanity.com/paper/2507.11762/) (2025)
- [Differentially Private Linear Regression and Synthetic Data Generation with Statistical Guarantees](https://mlsanity.com/paper/2510.16974/) (2025)
- [Differentially Private E-Values](https://mlsanity.com/paper/2510.18654/) (2025)
- [Optimal Survey Design for Private Mean Estimation](https://mlsanity.com/paper/2501.18121/) (2025)
- [Noise-Calibrated Inference from Differentially Private Sufficient Statistics in Exponential Families](https://mlsanity.com/paper/2603.02010/) (2026)

## Abstract (arXiv)

The goal of this paper is to develop a practical and general-purpose approach to construct confidence intervals for differentially private parametric estimation. We find that the parametric bootstrap is a simple and effective solution. It cleanly reasons about variability of both the data sample and the randomized privacy mechanism and applies "out of the box" to a wide class of private estimation routines. It can also help correct bias caused by clipping data to limit sensitivity. We prove that the parametric bootstrap gives consistent confidence intervals in two broadly relevant settings, including a novel adaptation to linear regression that avoids accessing the covariate data multiple times. We demonstrate its effectiveness for a variety of estimators, and find that it provides confidence intervals with good coverage even at modest sample sizes and performs better than alternative approaches.