A unified approach for covariance matrix estimation under Stein loss

Anis  M. Haddouche; Wei Lu

doi:10.5802/crmath.356

Statistiques

A unified approach for covariance matrix estimation under Stein loss

Anis M. Haddouche ¹ ; Wei Lu ²

¹ INSA Rouen, Normandie Univ, UNIROUEN, UNIHAVRE, LITIS and LMI, avenue de l’Université, BP 8, Saint-Étienne-du-Rouvray, 76801, France
² INSA Rouen, Normandie Univ, UNIROUEN, UNIHAVRE, LMI, avenue de l’Université, BP 8, Saint-Étienne-du-Rouvray, 76801, France

Comptes Rendus. Mathématique, Volume 360 (2022), pp. 1093-1098.

Résumé
Abstract

Dans cet article, nous abordons le problème de l’estimation d’une matrice de covariance d’une distribution gaussienne multivariée, du point de vue de la théorie de la décision, par rapport à une fonction de coût de type Stein. Nous étudions dans une approche unifiée le cas où la matrice de covariance est inversible et le cas où elle n’est pas inversible.

In this paper, we address the problem of estimating a covariance matrix of a multivariate Gaussian distribution, from a decision theoretic point of view, relative to a Stein type loss function. We investigate the case where the covariance matrix is invertible and the case when it is non–invertible in a unified approach.

Reçu le : 2021-07-13
Révisé le : 2022-01-04
Accepté le : 2022-03-13
Publié le : 2022-10-04

DOI : 10.5802/crmath.356

Classification : 62H12, 62F10, 62C99

Affiliations des auteurs :

Anis M. Haddouche ¹ ; Wei Lu ²

¹ INSA Rouen, Normandie Univ, UNIROUEN, UNIHAVRE, LITIS and LMI, avenue de l’Université, BP 8, Saint-Étienne-du-Rouvray, 76801, France
² INSA Rouen, Normandie Univ, UNIROUEN, UNIHAVRE, LMI, avenue de l’Université, BP 8, Saint-Étienne-du-Rouvray, 76801, France

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

@article{CRMATH_2022__360_G10_1093_0,
     author = {Anis  M. Haddouche and Wei Lu},
     title = {A unified approach for covariance matrix estimation under {Stein} loss},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {1093--1098},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {360},
     year = {2022},
     doi = {10.5802/crmath.356},
     language = {en},
}

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Anis  M. Haddouche; Wei Lu. A unified approach for covariance matrix estimation under Stein loss. Comptes Rendus. Mathématique, Volume 360 (2022), pp. 1093-1098. doi : 10.5802/crmath.356. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.356/

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