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A unified approach for covariance matrix estimation under Stein loss
Anis M. Haddouche1   ; Wei Lu2
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.

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.

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DOI : 10.5802/crmath.356
Classification : 62H12, 62F10, 62C99

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 
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     title = {A unified approach for covariance matrix estimation under {Stein} loss},
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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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