Near-Optimal Private Tests for Simple and MLR Hypotheses

• URL: http://arxiv.org/abs/2601.21959v1
• Date: Thu, 29 Jan 2026 16:36:21 GMT
• Title: Near-Optimal Private Tests for Simple and MLR Hypotheses
• Authors: Yu-Wei Chen, Raghu Pasupathy, Jordan Awan,
• Abstract summary: We develop a near-optimal testing procedure under the framework of Gaussian differential privacy.<n>We construct private test statistics that achieve the same relative efficiency as the non-private, most powerful tests.<n>Our tests offer comparable power to the non-private most powerful tests, even at moderately small sample sizes and privacy loss budgets.
• Score: 13.738306418341729
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We develop a near-optimal testing procedure under the framework of Gaussian differential privacy for simple as well as one- and two-sided tests under monotone likelihood ratio conditions. Our mechanism is based on a private mean estimator with data-driven clamping bounds, whose population risk matches the private minimax rate up to logarithmic factors. Using this estimator, we construct private test statistics that achieve the same asymptotic relative efficiency as the non-private, most powerful tests while maintaining conservative type I error control. In addition to our theoretical results, our numerical experiments show that our private tests outperform competing DP methods and offer comparable power to the non-private most powerful tests, even at moderately small sample sizes and privacy loss budgets.

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