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pith:V2JCFZK2

pith:2026:V2JCFZK2TOC6PUQ6B5BQFPPIIF

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Weighted and Truncated Tail Index Estimation under Random Censoring: A Unified Full-Range Framework

Abdelhakim Necir, Djamel Meraghni, Nour Elhouda Guesmia

A weighted and truncated Nelson-Aalen process yields consistent extreme value index estimators valid for any strength of right censoring.

arxiv:2605.13650 v1 · 2026-05-13 · math.ST · stat.TH

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Claims

C1strongest claim

Under standard regular variation conditions, we establish a uniform Gaussian approximation and derive consistency and asymptotic normality without imposing restrictions on the censoring level.

C2weakest assumption

The tail distribution satisfies regular variation and the censoring mechanism permits the weighted truncated Nelson-Aalen process to possess the required uniform approximation properties; the linearization step and the choice of tuning parameter greater than one are taken as given without further qualification on their interaction with strong censoring.

C3one line summary

A unified full-range framework for tail-index estimation under random censoring that restores uniform Gaussian approximation and asymptotic normality for any censoring strength via a weighted truncated Nelson-Aalen process.

References

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[1] Basu, A., Harris, I. R., Hjort, N. L., & Jones, M. C. 1998. Robust and efficient estimation by minimizing a density power divergence. Biometrika, 85, 549--559 1998

[2] Bias reduced tail estimation for censored Pareto type distributions 2016

[3] Penalized bias reduction in extreme value estimation for censored Pareto-type data, and long-tailed insurance applications 2018

[4] Estimation of the extreme value index in a censorship framework: asymptotic and finite sample behavior 2019

[5] Bladt, M., Goegebeur, Y. and Guillou, A. (2025). Asymptotically unbiased estimator of the extreme value index under random censoring, https://hal.science/hal-04786783v2 2025

Receipt and verification

First computed	2026-05-18T02:44:17.489581Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ae9222e55a9b85e7d21e0f4302bde84150e9e9a0381f7da2b847583ab040a3a8

Aliases

arxiv: 2605.13650 · arxiv_version: 2605.13650v1 · doi: 10.48550/arxiv.2605.13650 · pith_short_12: V2JCFZK2TOC6 · pith_short_16: V2JCFZK2TOC6PUQ6 · pith_short_8: V2JCFZK2

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/V2JCFZK2TOC6PUQ6B5BQFPPIIF \
  | 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: ae9222e55a9b85e7d21e0f4302bde84150e9e9a0381f7da2b847583ab040a3a8

Canonical record JSON

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  "metadata": {
    "abstract_canon_sha256": "3001f26789e543d3662a4a172cf88a18ef3c6ce46af174389663ff48548d507d",
    "cross_cats_sorted": [
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    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.ST",
    "submitted_at": "2026-05-13T15:09:20Z",
    "title_canon_sha256": "b2e1347c0fba011912e3add06ce7cdabe83bfba46c44daf06fbb9f52c88b47bb"
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  "source": {
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    "kind": "arxiv",
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