Asymptotic Anytime-Valid Quantile Inference under Local Differential Privacy

2026-09-18

AI Summary

研究解决了局部差分隐私下顺序分位数推断难题，通过结合随机响应与动态链式并行随机梯度下降方法来实现。

Abstract

Sequential quantile inference is difficult under local differential privacy because every record is randomized before reaching the analyst and the limiting quantile variance depends on an unknown density. We develop an online procedure that combines randomized response with dynamically chained parallel stochastic gradient descent (P-SGD). The resulting Polyak--Ruppert estimator admits a strong Gaussian approximation. A cross-chain quadratic statistic, computed entirely from private iterates, consistently estimates the limiting variance without a separate online density estimator. These results yield asymptotic confidence sequences and, under polynomial chain growth, asymptotic time-uniform coverage. Arm-wise constructions support locally private quantile best-arm identification, time-uniform simple-regret bounds, and sequential A/B tests of quantile treatment effects. Simulations and salary-data analyses illustrate the finite-sample behavior and practical use of the proposed methods.

Problem

• local differential privacy
• sequential quantile inference
• randomized response

Innovation

• local differential privacy
• parallel stochastic gradient descent (P-SGD)
• asymptotic anytime-valid inference
• quantile inference
• Polyak--Ruppert estimator