Pith Number

pith:CGWCRL4E

pith:2026:CGWCRL4EHMBSI4NXTKR5SXXZXN

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The Threshold Breakdown Point

Marco Avella Medina, Tianjun Ke

The threshold breakdown point is the smallest contamination fraction that forces an estimator past a chosen deviation level.

arxiv:2605.04317 v2 · 2026-05-05 · math.ST · stat.TH

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Claims

C1strongest claim

We define the threshold breakdown point, the smallest contamination fraction needed to induce a prescribed deviation, and the finite sample m-sensitivity, the worst-case deviation that an estimator can incur after m observations are contaminated. We derive these measures for commonly used M-estimators, their standard errors and related test statistics.

C2weakest assumption

The derivations and extensions assume that M-estimators satisfy the regularity conditions needed for explicit breakdown calculations and that the contamination model permits well-defined worst-case deviations; the inferential results further assume standard asymptotic conditions for consistency, normality, and bootstrap validity.

C3one line summary

Introduces threshold breakdown point and m-sensitivity as new finite-sample robustness measures for M-estimators and tests, with consistency, asymptotic normality, and multiplier bootstrap inference.

Receipt and verification

First computed	2026-05-20T00:03:13.857049Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

11ac28af843b032471b79aa3d95ef9bb570cd7acf0605be07253f1564c8c9e31

Aliases

arxiv: 2605.04317 · arxiv_version: 2605.04317v2 · doi: 10.48550/arxiv.2605.04317 · pith_short_12: CGWCRL4EHMBS · pith_short_16: CGWCRL4EHMBSI4NX · pith_short_8: CGWCRL4E

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/CGWCRL4EHMBSI4NXTKR5SXXZXN \
  | 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: 11ac28af843b032471b79aa3d95ef9bb570cd7acf0605be07253f1564c8c9e31

Canonical record JSON

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  "metadata": {
    "abstract_canon_sha256": "199f96891f2716bd20ae5fff4653ca87a40c22a656be20a77baeb1355485df92",
    "cross_cats_sorted": [
      "stat.TH"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.ST",
    "submitted_at": "2026-05-05T21:36:45Z",
    "title_canon_sha256": "4e5894fa65d76ed2a71e6d3dd412f7b8bebaf756f4e4955302fff8b6a98b866e"
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    "kind": "arxiv",
    "version": 2
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