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Stable and efficient covariance estimation for sample L-moments using Hájek projections — arXiv:2610.41640

Source: arXiv (en)
Original: https://arxiv.org/abs/2610.41640
License (as archived): CC0-1.0
Archived: 2026-11-02T04:55:28.040Z
SHA-256 of the archived text: 151f81fcf585eba40170a5b8a325bbbbea6bf2341b4a4f6c3742ac3b1177a5a3
Stable URL of this page: https://metraipolis.com/documento/dc_64aeb65a2dee

How to cite

Stable and efficient covariance estimation for sample L-moments using Hájek projections — arXiv:2610.41640 — arXiv (en), https://arxiv.org/abs/2610.41640 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_64aeb65a2dee (Metraipolis archive dc_64aeb65a2dee, sha256 151f81fcf585eba40170a5b8a325bbbbea6bf2341b4a4f6c3742ac3b1177a5a3)

BibTeX

@misc{dc64aeb65a2dee,
  title = {Stable and efficient covariance estimation for sample L-moments using Hájek projections — arXiv:2610.41640},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2610.41640},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_64aeb65a2dee; sha256 151f81fcf585eba40170a5b8a325bbbbea6bf2341b4a4f6c3742ac3b1177a5a3},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2610.41640. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

L-moments are useful summary statistics and are widely used in statistical analysis. The joint covariance matrix of sample L-moments not only describes their sampling uncertainty but is also needed for covariance-weighted distances and related statistical procedures. An exact unbiased covariance estimator is already available. However, in our previous applications, this estimator sometimes produced singular or indefinite covariance matrices. Such matrices cause problems when matrix inversion is required. The present paper addresses this difficulty. We examine standard positive-definite corrections and two covariance estimators based on leave-one-out sample L-moments: the delete-one jackknife estimator and an estimator based on the Hájek projection. Both are positive semidefinite by construction. Simulation results show that the projection estimator generally has smaller estimation error and better numerical stability than the exact unbiased estimator. The jackknife estimator overestimates the variances of higher-order sample L-moments and has larger estimation error than the projection estimator. We also develop fast rank-prefix algorithms for the three covariance estimators considered. These algorithms substantially reduce computation time.

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/2610.41640 — 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 2026-11-02T04:46:12.637Z dalla pagina https://arxiv.org/list/stat.ME/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).