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The Missing Corner: When Sharp Causal Bounds Fail to Compose — arXiv:2610.08197

Source: arXiv (en)
Original: https://arxiv.org/abs/2610.08197
License (as archived): CC0-1.0
Archived: 2026-10-07T11:46:29.369Z
SHA-256 of the archived text: 65843e244059f902bffdf081361a199b58fce26606cd1ba61e29079cbf7b934e
Stable URL of this page: https://metraipolis.com/documento/dc_cebd571bf296

How to cite

The Missing Corner: When Sharp Causal Bounds Fail to Compose — arXiv:2610.08197 — arXiv (en), https://arxiv.org/abs/2610.08197 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_cebd571bf296 (Metraipolis archive dc_cebd571bf296, sha256 65843e244059f902bffdf081361a199b58fce26606cd1ba61e29079cbf7b934e)

BibTeX

@misc{dccebd571bf296,
  title = {The Missing Corner: When Sharp Causal Bounds Fail to Compose — arXiv:2610.08197},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2610.08197},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_cebd571bf296; sha256 65843e244059f902bffdf081361a199b58fce26606cd1ba61e29079cbf7b934e},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2610.08197. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Sharp bounds on two potential-outcome means need not combine into sharp bounds on their difference. We characterize exactly when composition is guaranteed across environments sharing a joint potential-outcome law. For binary treatment and outcome, fix strict selection-probability bounds and interior treatment propensities. Subtracting the full model's sharp mean intervals gives sharp average-treatment-effect bounds for every compatible observed law if and only if the absolute selection bounds coincide across environments. Under this alignment, the complete mean region is rectangular; its endpoints and attaining causal models require $O(K)$ arithmetic operations for $K$ environments. For every mismatch, failure occurs on a relatively open set of positive observed tables at the prescribed propensities and persists under small joint drift. We give computable perturbation certificates and an exact family whose gap is first order in the mismatch. A separate finite-confounding family shows when the lost joint information changes an identified causal sign. These results distinguish local marginal sharpness from joint attainability after combining environments.

Tema degli esploratori: statistica e scienza dei dati (elenco arXiv stat.ME, nuovi lavori del giorno).
Categorie arXiv: Methodology (stat.ME).
Pagina del lavoro: https://arxiv.org/abs/2610.08197 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-07T11:20:24.687Z dalla pagina https://arxiv.org/list/stat.ME/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).