Pith Number

pith:FIAKPDHV

pith:2026:FIAKPDHVGSJVLZKLJSYVI77KHZ

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How long should a block be?

Anthony C. Davison, L\'eo R. Belzile

Excessively long blocks reduce asymptotic relative efficiency in the block maxima method, and likelihood-based diagnostics can identify suitable lengths even with rounded or censored data.

arxiv:2605.12760 v1 · 2026-05-12 · stat.ME · stat.AP

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\pithnumber{FIAKPDHVGSJVLZKLJSYVI77KHZ}

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2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

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The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

Taking excessively long blocks reduces asymptotic relative efficiency, and likelihood-based approaches together with graphical diagnostics can determine whether a proposed block length is suitable, allowing for rounding and left-censoring.

C2weakest assumption

The data-generating process is close enough to the domain of attraction of a non-degenerate extreme-value limit that the block-maxima approximation remains useful once m is large enough; this is invoked throughout the efficiency calculations and diagnostic derivations.

C3one line summary

Excessively long blocks lower asymptotic relative efficiency in the block-maxima method, and new likelihood and diagnostic procedures are proposed to check whether a chosen length is adequate under rounding or censoring.

References

61 extracted · 61 resolved · 1 Pith anchors

[1] P. Prescott and A. T. Walden , year = 1980, journal = 1980

[2] Mathematical Proceedings of the Cambridge Philosophical Society , volume = 24, number = 2, pages =

[3] Revue math\'

[4] Annals of Mathematics44(3), 423–453 (1943) https://doi.org/10.2307/1968974 1943 · doi:10.2307/1968974

[5] Bulletin of the American Mathematical Society , volume = 54, pages = 1948 · doi:10.1090/s0002-9904-1948-08936-4

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-18T03:09:48.443229Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2a00a78cf5349355e54b4cb1547fea3e63ce6038ca052bf0d0813c1d1b50f1f0

Aliases

arxiv: 2605.12760 · arxiv_version: 2605.12760v1 · doi: 10.48550/arxiv.2605.12760 · pith_short_12: FIAKPDHVGSJV · pith_short_16: FIAKPDHVGSJVLZKL · pith_short_8: FIAKPDHV

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/FIAKPDHVGSJVLZKLJSYVI77KHZ \
  | 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: 2a00a78cf5349355e54b4cb1547fea3e63ce6038ca052bf0d0813c1d1b50f1f0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7f2f9ece17f41f595e5a06d7c92cabde4d2f148579eab608ec4f18cd6afcd3c9",
    "cross_cats_sorted": [
      "stat.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "stat.ME",
    "submitted_at": "2026-05-12T21:14:09Z",
    "title_canon_sha256": "f618a9b6e35d8f10f9ab12b169fc8af404a005ae199c98eceeb13ce67b7bcb66"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.12760",
    "kind": "arxiv",
    "version": 1
  }
}