Title: Near-Optimal Private Tests for Simple and MLR Hypotheses

Abstract:

This study introduces a near-optimal testing framework utilizing Gaussian differential privacy, designed for both simple hypotheses and one- or two-sided tests involving monotone likelihood ratio conditions. The proposed mechanism relies on a private mean estimator that employs data-driven clamping bounds, ensuring that its population risk aligns with the private minimax rate, modulo logarithmic factors. By leveraging this estimator, we formulate private test statistics that preserve the asymptotic relative efficiency of their non-private, most powerful counterparts, all while guaranteeing conservative control over type I error rates. Beyond these theoretical contributions, our numerical evaluations demonstrate that the proposed private tests surpass alternative differentially private methods. Furthermore, they exhibit statistical power comparable to non-private most powerful tests, even when operating with moderately small sample sizes and limited privacy loss budgets.

Source: arXiv Generated at: 2026-06-02 00:00:00 UTC