Pith Number

pith:3VQPTFQP

pith:2025:3VQPTFQP3OFUDAWKB37PUW4YOQ

not attested not anchored not stored refs resolved

The post-hoc test for local dependence

Bart{\l}omiej Gibas, Bogdan \'Cmiel

A test based on the quantile dependence function uses critical surfaces to detect local dependence while preserving the global significance level.

arxiv:2512.20280 v2 · 2025-12-23 · stat.ME

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{3VQPTFQP3OFUDAWKB37PUW4YOQ}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

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

Relying on copula-based results, we introduce a novel method for testing global and local statistical independence using the quantile dependence function. ... we introduce so-called critical surfaces that guaranty a locally equal probability of exceeding them under independence. This approach enables a detailed examination of local discrepancies and an assessment of their statistical significance while preserving the overall significance level of the test.

C2weakest assumption

The method assumes that copula-based results for the quantile dependence function are valid for the data at hand and that the critical surfaces can be constructed to deliver exactly equal local exceedance probabilities under independence without additional distributional assumptions.

C3one line summary

A new testing procedure uses critical surfaces on the quantile dependence function to detect local dependence while preserving the global significance level.

References

23 extracted · 23 resolved · 2 Pith anchors

[1] Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

[2] Main results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

[3] Numerical results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 3.1. Comparison of Empirical Power . . . . . . . . . . . . . . .

[4] References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2

[5] ,(Xn, Yn) withajointdistributionHandcontinuousmarginaldistributionsFandG, respectively

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-18T02:44:32.047209Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dd60f9960fdb8b4182ca0efefa5b9874023e7a5d8b381fd4adef2e1d9171b2a3

Aliases

arxiv: 2512.20280 · arxiv_version: 2512.20280v2 · doi: 10.48550/arxiv.2512.20280 · pith_short_12: 3VQPTFQP3OFU · pith_short_16: 3VQPTFQP3OFUDAWK · pith_short_8: 3VQPTFQP

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/3VQPTFQP3OFUDAWKB37PUW4YOQ \
  | 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: dd60f9960fdb8b4182ca0efefa5b9874023e7a5d8b381fd4adef2e1d9171b2a3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e034aa9a3e97f708fa71235a27e9649aac686e60d458272d2659e4d8526e111b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "stat.ME",
    "submitted_at": "2025-12-23T11:39:31Z",
    "title_canon_sha256": "38d0e9c7a31af7055818c8a0b73d74a64cb7042c26e5aabc792da52e8943bb58"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2512.20280",
    "kind": "arxiv",
    "version": 2
  }
}