{"paper":{"title":"Multiple Testing of One-Sided Hypotheses with Conservative $p$-values","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Estimating the marginal null distribution via empirical Bayes produces refined p-values that plug directly into standard multiple testing procedures for one-sided hypotheses.","cross_cats":[],"primary_cat":"stat.ME","authors_text":"Hyungwon Choi, Jaesik Jeong, Johan Lim, Kwangok Seo","submitted_at":"2025-12-31T03:26:43Z","abstract_excerpt":"We study a large-scale one-sided multiple testing problem in which test statistics follow normal distributions with unit variance, and the goal is to identify signals with positive mean effects. A conventional approach is to compute $p$-values under the assumption that all null means are exactly zero and then apply standard multiple testing procedures such as the Benjamini-Hochberg (BH) or Storey-BH method. However, because the null hypothesis is composite, some null means may be strictly negative. In this case, the resulting $p$-values are conservative, leading to a substantial loss of power."},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"we estimate the marginal null distribution of the test statistics within an empirical Bayes framework and construct refined p-values based on this estimated distribution. These refined p-values can then be directly used in standard multiple testing procedures without modification.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The marginal null distribution of the test statistics can be accurately estimated from the observed data using empirical Bayes, under the maintained assumption that test statistics are normal with unit variance.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Estimating the marginal null distribution via empirical Bayes produces refined p-values that restore power in one-sided multiple testing when conventional p-values are conservative due to negative null means.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Estimating the marginal null distribution via empirical Bayes produces refined p-values that plug directly into standard multiple testing procedures for one-sided hypotheses.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"a8ccb5ac84c76dc2c3441fe2a8304c3b97908e65c7b64c76c07e6484f76470bc"},"source":{"id":"2512.24588","kind":"arxiv","version":2},"verdict":{"id":"048935d4-f105-4121-ba2e-7db0f2a7e6ac","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-16T19:27:14.855194Z","strongest_claim":"we estimate the marginal null distribution of the test statistics within an empirical Bayes framework and construct refined p-values based on this estimated distribution. These refined p-values can then be directly used in standard multiple testing procedures without modification.","one_line_summary":"Estimating the marginal null distribution via empirical Bayes produces refined p-values that restore power in one-sided multiple testing when conventional p-values are conservative due to negative null means.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The marginal null distribution of the test statistics can be accurately estimated from the observed data using empirical Bayes, under the maintained assumption that test statistics are normal with unit variance.","pith_extraction_headline":"Estimating the marginal null distribution via empirical Bayes produces refined p-values that plug directly into standard multiple testing procedures for one-sided hypotheses."},"references":{"count":18,"sample":[{"doi":"","year":1985,"title":"Azzalini, A. (1985). A class of distributions which includes the normal ones.Scandinavian Journal of Statistics 12(2), 171–178","work_id":"a0b91719-3ef8-4e41-9e7a-8974b6cdcb37","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2019,"title":"Barber, R. F. and E. J. Cand` es (2019). A knockoff filter for high-dimensional selective inference","work_id":"4fb972b3-493f-42c2-b981-13dcfe7c959a","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1995,"title":"Benjamini, Y. and Y. Hochberg (1995). Controlling the false discovery rate: a practical and powerful approach to multiple testing.Journal of the Royal statistical society: series B (Method- ological) ","work_id":"5015034b-f251-42d2-971d-16f60fd201f8","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2013,"title":"Brent, R. P. (2013).Algorithms for minimization without derivatives. Courier Corporation","work_id":"b898fb18-4d7a-4801-9fe9-f4d7022e5642","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2023,"title":"de U˜ na-´Alvarez, J. (2023). Controlling the number of significant effects in multiple testing. arXiv preprint arXiv:2311.00885","work_id":"bd3be860-dc13-480d-a003-731fe68ae1ff","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":18,"snapshot_sha256":"6f32d4088a5ede4d93344e4bd37cc60db53beca18e152fa216b9f7cb6fa7f3ce","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"}