# Online Local Differential Private Quantile Inference via Self-normalization

arXiv: https://arxiv.org/abs/2306.10260 · HTML: https://mlsanity.com/paper/2306.10260/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Jun 2023.

## Built on by (most cited first, 5 of 5)

- [Exactly Minimax-Optimal Locally Differentially Private Sampling](https://mlsanity.com/paper/2410.22699/) (2024)
- [Federated Learning of Quantile Inference under Local Differential Privacy](https://mlsanity.com/paper/2509.21800/) (2025)
- [How Much is Left? LLMs Linearly Encode Their Remaining Output Length](https://mlsanity.com/paper/2607.05316/) (2026)
- [Uncertainty quantification by block bootstrap for differentially private stochastic gradient descent](https://mlsanity.com/paper/2405.12553/) (2024)
- [Locally Private Inference for Riemannian Stochastic Optimization](https://mlsanity.com/paper/2609.22642/) (2026)

## Abstract (arXiv)

Based on binary inquiries, we developed an algorithm to estimate population quantiles under Local Differential Privacy (LDP). By self-normalizing, our algorithm provides asymptotically normal estimation with valid inference, resulting in tight confidence intervals without the need for nuisance parameters to be estimated. Our proposed method can be conducted fully online, leading to high computational efficiency and minimal storage requirements with O(1) space. We also proved an optimality result by an elegant application of one central limit theorem of Gaussian Differential Privacy (GDP) when targeting the frequently encountered median estimation problem. With mathematical proof and extensive numerical testing, we demonstrate the validity of our algorithm both theoretically and experimentally.