{"paper":{"title":"Gaussian Differentially Private $e$-values: Construction, Threshold Calibration, and Multiple Testing","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"stat.ME","authors_text":"Bowen Gang, Qi Kuang, Yin Xia","submitted_at":"2026-05-28T05:41:52Z","abstract_excerpt":"This paper develops a framework for differentially private $e$-values under Gaussian differential privacy ($\\mu$-GDP). We characterize the canonical noise mechanism, establishing that optimal multiplicative perturbation follows a Gaussian distribution. Using this distribution, we derive a globally sharp rejection threshold that strictly improves upon the standard Markov bound. Asymptotic analysis shows that in low-sensitivity regimes, the calibrated private test achieves a net power gain over the non-private baseline. For multiple testing, we introduce a recursive peeling algorithm that adapti"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.29388","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.29388/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}