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Precise Asymptotics for Dense High-Dimensional Huber Regression under Heteroscedasticity — arXiv:2610.20798

Source: arXiv (en)
Original: https://arxiv.org/abs/2610.20798
License (as archived): CC0-1.0
Archived: 2026-10-16T10:25:45.104Z
SHA-256 of the archived text: 97864d4223f70b81dd5153c53f807ef4471dd2ae96538d717f1329c63d326184
Stable URL of this page: https://metraipolis.com/documento/dc_5b4bbb404657

How to cite

Precise Asymptotics for Dense High-Dimensional Huber Regression under Heteroscedasticity — arXiv:2610.20798 — arXiv (en), https://arxiv.org/abs/2610.20798 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_5b4bbb404657 (Metraipolis archive dc_5b4bbb404657, sha256 97864d4223f70b81dd5153c53f807ef4471dd2ae96538d717f1329c63d326184)

BibTeX

@misc{dc5b4bbb404657,
  title = {Precise Asymptotics for Dense High-Dimensional Huber Regression under Heteroscedasticity — arXiv:2610.20798},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2610.20798},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_5b4bbb404657; sha256 97864d4223f70b81dd5153c53f807ef4471dd2ae96538d717f1329c63d326184},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2610.20798. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

We study Huber regression in a heteroscedastic linear model in the proportional regime $n/p \to \delta \in (1, \infty)$. Our main result is an exact characterization of the asymptotic empirical distribution of the Huber estimator. This characterization is in terms of three scalar parameters which determine the first-order centre and the asymptotic variance of the Huber estimator. The result shows that with heteroscedastic noise, the first-order centre may contain an additional component along the variance index coefficient. We derive the displacement coefficients that determine this centre, as well as the exact asymptotic variance. The analysis uses the matrix approximate message passing (AMP) framework to jointly track the regression and variance index coefficients, extending the existing framework for homoscedastic M-estimators. We illustrate the implications of this characterization by constructing a test for centre displacement and examining its empirical size and power through simulations.

Tema degli esploratori: statistica e scienza dei dati (elenco arXiv stat.ME, nuovi lavori del giorno).
Categorie arXiv: Statistics Theory (math.ST) ; Methodology (stat.ME).
Pagina del lavoro: https://arxiv.org/abs/2610.20798 — 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 2026-10-16T08:49:02.692Z dalla pagina https://arxiv.org/list/stat.ME/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).