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pith:5NN7HTT5

pith:2026:5NN7HTT5MV452CVGK5CXJYGHFC

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Pattern-based tests for two-dimensional copulas

L. Baringhaus, R. Gr\"ubel

A functional central limit theorem for pattern frequencies in bivariate rank plots enables nonparametric copula tests.

arxiv:2605.13710 v1 · 2026-05-13 · math.ST · stat.TH

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Claims

C1strongest claim

We obtain a functional central limit theorem for such pattern frequencies in the context of two-dimensional random samples. The result serves as the basis for nonparametric goodness-of-fit tests, for two-sample tests, and for tests of symmetry.

C2weakest assumption

The two-dimensional samples are i.i.d. from a continuous bivariate distribution, permitting the rank plot to be treated as a discrete copula whose pattern frequencies converge in the permuton topology.

C3one line summary

A functional central limit theorem for pattern frequencies in 2D samples enables nonparametric goodness-of-fit, two-sample, and symmetry tests for copulas, with bootstrap critical values and parametric examples.

References

52 extracted · 52 resolved · 0 Pith anchors

[1] More asymmetry yields faster matrix multiplication 1971 · doi:10.1137/1

[2] Baringhaus, L. (1994). On a modification of the Hoeffding–Blum–Kiefer–Rosenblatt independence criterion. Comm. Statist. Simulation Comput.23683–689. https://doi.org/10.1080/03610919408813193 1994 · doi:10.1080/03610919408813193

[3] Baringhaus, L., Franz, C. (2004). On a new multivariate two-sample test.J. Multivariate Anal.88190–206. https://doi.org/10.1016/S0047-259X(03)00079-4 2004 · doi:10.1016/s0047-259x(03)00079-4

[4] Baringhaus, L., Franz, C. (2010). Rigid motion invariant two-sample tests.Statist. Sinica201333–1361. Tests for copulas 25 2010

[5] Baringhaus, L., Grübel, R. (2024). Random permutations generated by delay models and estimation of delay distributions.Electron. J. Stat.18167–190. https://doi.org/10.1214/23-EJS2205 2024 · doi:10.1214/23-ejs2205

Receipt and verification

First computed	2026-05-18T02:44:16.761709Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

eb5bf3ce7d6579dd0aa6574574e0c7288bdf9da51d60eaa1cc00730d20d67999

Aliases

arxiv: 2605.13710 · arxiv_version: 2605.13710v1 · doi: 10.48550/arxiv.2605.13710 · pith_short_12: 5NN7HTT5MV45 · pith_short_16: 5NN7HTT5MV452CVG · pith_short_8: 5NN7HTT5

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curl -sH 'Accept: application/ld+json' https://pith.science/pith/5NN7HTT5MV452CVGK5CXJYGHFC \
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# expect: eb5bf3ce7d6579dd0aa6574574e0c7288bdf9da51d60eaa1cc00730d20d67999

Canonical record JSON

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