Pith Number

pith:3PKIGHOZ

pith:2026:3PKIGHOZ6JIGHHSYTPLNBRYYC3

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Variance Inference Beyond the Sandwich for Asymptotically Linear Estimators with Second-Order Remainders

Lin Li, Pengcheng Wu

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.

arxiv:2603.14561 v5 · 2026-03-15 · stat.ME · math.ST · stat.TH

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Claims

C1strongest 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.

C2weakest 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.

C3one 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.

Formal links

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Receipt and verification

First computed	2026-05-26T01:02:33.284497Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dbd4831dd9f250639e589bd6d0c71816d1c26f3ebac95f710bacc00efb5238ae

Aliases

arxiv: 2603.14561 · arxiv_version: 2603.14561v5 · doi: 10.48550/arxiv.2603.14561 · pith_short_12: 3PKIGHOZ6JIG · pith_short_16: 3PKIGHOZ6JIGHHSY · pith_short_8: 3PKIGHOZ

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curl -sH 'Accept: application/ld+json' https://pith.science/pith/3PKIGHOZ6JIGHHSYTPLNBRYYC3 \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: dbd4831dd9f250639e589bd6d0c71816d1c26f3ebac95f710bacc00efb5238ae

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "39998f7608f61ab59b74c03e683bc3215836c03e5942426f331da1adbf45b51b",
    "cross_cats_sorted": [
      "math.ST",
      "stat.TH"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "stat.ME",
    "submitted_at": "2026-03-15T19:23:26Z",
    "title_canon_sha256": "c1b4f8290610ac1f82ca8691ce426951fc5c32d0ab1c20052688a52dfd86c916"
  },
  "schema_version": "1.0",
  "source": {
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    "kind": "arxiv",
    "version": 5
  }
}