Skip to content
DraconiticResearch
Search Sources API
182,544 studies31 sourcesUpdated 26 min ago
PreprintarXiv licencearXiv

The exact dimensional threshold for Spearman rank-correlation compatibility

  • Ruodu Wang
  • Zhenyuan Zhang
Open at sourcePDFDOICite

Abstract

We show that, for a given dimension, the set of Spearman's rank correlation matrices and that of linear correlation matrices coincide if and only if the dimension is no larger than nine. For this, we construct an extreme rank-four counterexample in dimension ten and prove its incompatibility using moment identities and Cauchy-Schwarz. Appending unit directions produces counterexamples in every higher dimension. This, together with existing results, completes the dimensional classification and settles a long-standing open question in quantitative risk management.

Related

  1. The exact region determined by Spearman's rho and Gini's gamma
    Jonathan Ansari, Marcus Rockel, Stefanie Steinmaßl
    arXivPreprintarXiv licenceFull textStatisticsarXiv
  2. The exact region determined by Blomqvist's beta, Spearman's footrule and Kendall's tau
    Liljana Ferbar Tratar, Damjana Kokol Bukovšek, Blaž Mojškerc +3
    arXivPreprintarXiv licenceFull textStatisticsarXiv
  3. Deep Reinforcement Learning on Item-Compatibility Graphs for One-Dimensional Bin Packing
    M. Aslı Aydın
    arXivPreprintarXiv licenceFull textOptimisation & controlarXiv
  4. Near-Quadratic Error-Free Graph Matching above Otter's Threshold via Approximate Local Tree Correlation Testing
    Jiale Cheng, Ziao Wang, Lei Ying
    arXivPreprintCC BY 4.0Full textStatisticsarXiv
  5. The Exact Degree Threshold for Complement Connectivity
    Arsen Berk Tekdaş
    arXivPreprintarXiv licenceFull textCombinatorics & discrete mathematicsarXiv

Cite

BibTeXRIS
BibTeX
@misc{wang2026exact,
  title = {{The exact dimensional threshold for Spearman rank-correlation compatibility}},
  author = {Ruodu Wang and Zhenyuan Zhang},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.16278},
  eprint = {2609.16278},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.16278},
}
RIS
TY  - UNPB
TI  - The exact dimensional threshold for Spearman rank-correlation compatibility
AU  - Ruodu Wang
AU  - Zhenyuan Zhang
PY  - 2026
DA  - 2026/09/01
PB  - arXiv
DO  - 10.48550/arxiv.2609.16278
UR  - https://arxiv.org/abs/2609.16278
AB  - We show that, for a given dimension, the set of Spearman's rank correlation matrices and that of linear correlation matrices coincide if and only if the dimension is no larger than nine. For this, we construct an extreme rank-four counterexample in dimension ten and prove its incompatibility using moment identities and Cauchy-Schwarz. Appending unit directions produces counterexamples in every higher dimension. This, together with existing results, completes the dimensional classification and settles a long-standing open question in quantitative risk management.
ER  -