{"paper":{"title":"Variance Inference Beyond the Sandwich for Asymptotically Linear Estimators with Second-Order Remainders","license":"http://creativecommons.org/licenses/by/4.0/","headline":"When the second-order remainder adds non-negligible variance to asymptotically linear estimators, the sandwich variance underestimates total sampling variability but the leave-one-out jackknife and pairs bootstrap recover it.","cross_cats":["math.ST","stat.TH"],"primary_cat":"stat.ME","authors_text":"Lin Li, Pengcheng Wu","submitted_at":"2026-03-15T19:23:26Z","abstract_excerpt":"Semiparametric estimators admitting a von Mises expansion often reduce inference to the influence-function variance. This reduction is justified when the second-order remainder is negligible in variance, a condition that is stronger than the usual product-rate requirement guaranteeing classical asymptotic linearity. When the remainder contributes non-negligible variance, the standard sandwich can underestimate the total sampling variance and Wald intervals can undercover; we call this the \\emph{near-boundary regime}. We derive a finite-sample variance decomposition separating influence-functio"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We derive a finite-sample variance decomposition separating influence-function and remainder components, give a practical characterization of when sandwich variance can fail, and show that the leave-one-out jackknife and pairs cluster bootstrap can estimate the total variance under explicit regularity conditions.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The second-order remainder contributes non-negligible variance (the near-boundary regime), together with the regularity conditions required for jackknife self-normalization consistency and Mallows-2 bootstrap consistency; these conditions are stated but their verification in new applications is left to the user.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"When second-order remainders contribute variance in asymptotically linear estimators, sandwich variance underestimates the total; jackknife and bootstrap recover it for improved coverage.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"When the second-order remainder adds non-negligible variance to asymptotically linear estimators, the sandwich variance underestimates total sampling variability but the leave-one-out jackknife and pairs bootstrap recover it.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"6c2818b40d2c1c51dc71286484a703635fe912c8e792845689a24e11b88f039a"},"source":{"id":"2603.14561","kind":"arxiv","version":5},"verdict":{"id":"afbbff08-93d4-4115-8af0-897b07de7756","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-15T11:15:43.839135Z","strongest_claim":"We derive a finite-sample variance decomposition separating influence-function and remainder components, give a practical characterization of when sandwich variance can fail, and show that the leave-one-out jackknife and pairs cluster bootstrap can estimate the total variance under explicit regularity conditions.","one_line_summary":"When second-order remainders contribute variance in asymptotically linear estimators, sandwich variance underestimates the total; jackknife and bootstrap recover it for improved coverage.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The second-order remainder contributes non-negligible variance (the near-boundary regime), together with the regularity conditions required for jackknife self-normalization consistency and Mallows-2 bootstrap consistency; these conditions are stated but their verification in new applications is left to the user.","pith_extraction_headline":"When the second-order remainder adds non-negligible variance to asymptotically linear estimators, the sandwich variance underestimates total sampling variability but the leave-one-out jackknife and pairs bootstrap recover it."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2603.14561/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":2,"snapshot_sha256":"7134b041d5104fc19240aebaf2f45969beebb7412b9c7103993a7b4ed32de0c7"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}