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Generalized Linear Models for Extremes: Estimation and Inference in High Dimensions — arXiv:2608.16137

Source: arXiv (en)
Original: https://arxiv.org/abs/2608.16137
License (as archived): CC0-1.0
Archived: 2026-10-18T20:04:33.912Z
SHA-256 of the archived text: 6089803816ac914c72d4782cecabbd83715d0c366333b5ac06aada5f47014a8a
Stable URL of this page: https://metraipolis.com/documento/dc_7304efbaf39b

How to cite

Generalized Linear Models for Extremes: Estimation and Inference in High Dimensions — arXiv:2608.16137 — arXiv (en), https://arxiv.org/abs/2608.16137 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_7304efbaf39b (Metraipolis archive dc_7304efbaf39b, sha256 6089803816ac914c72d4782cecabbd83715d0c366333b5ac06aada5f47014a8a)

BibTeX

@misc{dc7304efbaf39b,
  title = {Generalized Linear Models for Extremes: Estimation and Inference in High Dimensions — arXiv:2608.16137},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2608.16137},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_7304efbaf39b; sha256 6089803816ac914c72d4782cecabbd83715d0c366333b5ac06aada5f47014a8a},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2608.16137. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

We propose a regression model for the extreme tail of a response variable, in which covariates rescale the tail without changing its shape. A single covariate-dependent function then characterizes the entire conditional tail, in contrast to extreme quantile regression, which targets a quantile at a pre-specified level. The tail shape itself is left unrestricted: heavy-, light- and short-tailed responses are covered by the same framework. We specify the function through a link function and a linear combination of the covariates, which is in the spirit of a generalized linear model. In estimation, we match the parametric specification to the underlying tail function under a Bregman divergence, over a region localized at the largest observations. The resulting loss is convex, and an $\ell_1$-penalty allows the number of covariates to exceed the effective sample size. The tail localization makes the asymptotic theory deviate from that for classical penalized generalized linear models. Only the tail observations selected by a random threshold are used in the statistical analysis, making them dependent. We derive the convergence rate of the penalized estimator and propose a debiased estimator that is asymptotically normal, yielding confidence intervals for individual coefficients. Its asymptotic variance is determined by the covariance of the score, which under tail localization differs from the Hessian and must be estimated separately. We apply the method to automobile insurance claims data.

Tema degli esploratori: statistica e scienza dei dati (retro-catalogo arXiv: annunci del 2026-08-18 in stat.ME).
Categorie arXiv: Methodology (stat.ME).
Pagina del lavoro: https://arxiv.org/abs/2608.16137 — 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 2026-10-18T19:44:19.572Z dalla pagina https://arxiv.org/catchup/stat.ME/2026-08-18?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).