Pith Number

pith:UXUES5S4

pith:2026:UXUES5S4ZXIAD35C7PCTWSAFTC

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Multivariate EDF tests for uniformity, normality,spherical and elliptical symetry, and independence based on a Brownian sheet deconstruction

Alejandra Caba\~na, Enrique M. Caba\~na

New EDF tests reduce multivariate normality, symmetry, and independence checks to uniformity testing on the unit hypercube via Brownian sheet decomposition.

arxiv:2605.17474 v1 · 2026-05-17 · math.ST · stat.ME · stat.TH

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Claims

C1strongest claim

Empirical power comparisons show that these extended procedures are highly competitive with existing methods in the statistical literature, demonstrating particular sensitivity to coordinate-based dependencies and joint dependency structures.

C2weakest assumption

Whenever a null hypothesis implies a joint distribution that factorizes into independent continuous components after a suitable mapping, the problem can be reduced to a uniformity test on the hypercube via componentwise probability integral transforms.

C3one line summary

Extends m-test and s-test via Brownian sheet deconstruction to new EDF procedures for uniformity on S^p, multivariate normality, symmetry, and independence, with competitive empirical power.

References

22 extracted · 22 resolved · 0 Pith anchors

[1] A. Caba˜ na, E. M. Caba˜ na, Brownian sheet and uniformity tests on the hypercube, to appear in Statistica.arXiv:2509.06134. URLhttps://arxiv.org/abs/2509.06134

[2] A. Caba˜ na, E. M. Caba˜ na, Multivariate tests of uniformity, normality, sym- metry and independence, r package, version 0.2.0. URLhttps://github.com/emcabana/MuniCandS

[3] Durbin, Distribution Theory for Tests Based on the Sample Distribu- tion Function, no 1973 · doi:10.1137/1.9781611970568

[4] A. Banerjee, I. S. Dhillon, J. Ghosh, S. Sra, Clustering on the unit hyper- sphere using von mises–fisher distributions, Journal of Machine Learning Research 6 (Sep) (2005) 1345–1382 2005

[5] URLhttps://www.R-project.org/ 2025

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Receipt and verification

First computed	2026-05-20T00:04:40.878147Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a5e849765ccdd001efa2fbc53b480598b81351125f863a995857ebfb2ba06283

Aliases

arxiv: 2605.17474 · arxiv_version: 2605.17474v1 · doi: 10.48550/arxiv.2605.17474 · pith_short_12: UXUES5S4ZXIA · pith_short_16: UXUES5S4ZXIAD35C · pith_short_8: UXUES5S4

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/UXUES5S4ZXIAD35C7PCTWSAFTC \
  | 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: a5e849765ccdd001efa2fbc53b480598b81351125f863a995857ebfb2ba06283

Canonical record JSON

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      "stat.TH"
    ],
    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
    "primary_cat": "math.ST",
    "submitted_at": "2026-05-17T14:22:46Z",
    "title_canon_sha256": "8022d6f84bc4fb5b03035f94bea2c9c73cc36d8ea4223e264d6492562fc0e376"
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