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Choosing the penalty in nonparametric regression: short and long-range dependence — arXiv:2609.29231

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.29231
License (as archived): CC0-1.0
Archived: 2026-10-08T06:07:31.273Z
SHA-256 of the archived text: f81313c3266ccf73dda6538cd5c1a070aa51965fa8fb3af4601e902a2b73bef8
Stable URL of this page: https://metraipolis.com/documento/dc_f04dbd7217ff

How to cite

Choosing the penalty in nonparametric regression: short and long-range dependence — arXiv:2609.29231 — arXiv (en), https://arxiv.org/abs/2609.29231 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_f04dbd7217ff (Metraipolis archive dc_f04dbd7217ff, sha256 f81313c3266ccf73dda6538cd5c1a070aa51965fa8fb3af4601e902a2b73bef8)

BibTeX

@misc{dcf04dbd7217ff,
  title = {Choosing the penalty in nonparametric regression: short and long-range dependence — arXiv:2609.29231},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.29231},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_f04dbd7217ff; sha256 f81313c3266ccf73dda6538cd5c1a070aa51965fa8fb3af4601e902a2b73bef8},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.29231. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

In this work, we study the one-dimensional regression problem under random design and Gaussian errors. Our framework is very general: we make no prior assumptions about the design (which may be nonstationary and exhibit short or long-range dependence), nor do we assume that the errors are homoscedastic. We examine in detail the cases where the error process exhibits short or long-range dependence. We adopt a least-squares penalized strategy using piecewise polynomials to estimate the regression function, following the framework of Baron, Birg{é} and Massart [1999]. We derive explicit penalties, up to calibration constants, to obtain adaptive estimators for which we establish risk bounds. Since these penalties depend on the dependence properties of the error process, which are unknown in practice, we propose several adaptations of the dimension jump calibration algorithm to make our procedures fully data-driven.

Tema degli esploratori: matematica e informatica teorica (retro-catalogo arXiv: annunci del 2026-09-25 in math.ST).
Categorie arXiv: Statistics Theory (math.ST).
Pagina del lavoro: https://arxiv.org/abs/2609.29231 — 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 2026-10-08T05:34:49.124Z dalla pagina https://arxiv.org/catchup/math.ST/2026-09-25?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).