{"paper":{"title":"Admissibility of Monotone Residual-Based Step-Down Multiple Testing Procedures Under Arbitrary Covariance Dependence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Arijit Chakrabarti, Prasenjit Ghosh","submitted_at":"2026-05-26T19:46:16Z","abstract_excerpt":"In this paper, we consider the problem of simultaneous testing of multivariate normal means under arbitrary covariance dependence. Specifically, let $\\vec{X}\\sim N_n(\\vec{\\theta},\\vec{\\Sigma})$, where $\\vec{\\theta}\\in\\mathbb{R}^n$ is unknown and $\\vec{\\Sigma}$ is a known positive definite covariance matrix. The objective is to test $H_{0i}:\\theta_i=0$ against $H_{Ai}:\\theta_i\\neq 0$, simultaneously for $i=1,\\ldots,n$. We establish a general admissibility theorem for a broad class of monotone residual-based step-down multiple testing procedures which iteratively rank the active hypotheses using"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.27625","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/2605.27625/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"}