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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@article{CRMATH_2022__360_G10_1093_0,
author = {Haddouche, Anis M. and Lu, Wei},
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},
number = {G10},
year = {2022},
doi = {10.5802/crmath.356},
language = {en},
url = {http://www.numdam.org/articles/10.5802/crmath.356/}
}
TY - JOUR AU - Haddouche, Anis M. AU - Lu, Wei TI - A unified approach for covariance matrix estimation under Stein loss JO - Comptes Rendus. Mathématique PY - 2022 SP - 1093 EP - 1098 VL - 360 IS - G10 PB - Académie des sciences, Paris UR - http://www.numdam.org/articles/10.5802/crmath.356/ DO - 10.5802/crmath.356 LA - en ID - CRMATH_2022__360_G10_1093_0 ER -
%0 Journal Article %A Haddouche, Anis M. %A Lu, Wei %T A unified approach for covariance matrix estimation under Stein loss %J Comptes Rendus. Mathématique %D 2022 %P 1093-1098 %V 360 %N G10 %I Académie des sciences, Paris %U http://www.numdam.org/articles/10.5802/crmath.356/ %R 10.5802/crmath.356 %G en %F CRMATH_2022__360_G10_1093_0
Haddouche, Anis M.; Lu, Wei. A unified approach for covariance matrix estimation under Stein loss. Comptes Rendus. Mathématique, Tome 360 (2022) no. G10, pp. 1093-1098. doi : 10.5802/crmath.356. http://www.numdam.org/articles/10.5802/crmath.356/
[1] Improved second order estimation in the singular multivariate normal model, J. Multivariate Anal., Volume 147 (2016), pp. 1-19 | DOI | MR | Zbl
[2] Estimation of a covariance matrix under Stein’s loss, Ann. Stat., Volume 13 (1985), pp. 1581-1591 | DOI | MR | Zbl
[3] Covariance matrix estimation under data-based loss, Stat. Probab. Lett., Volume 177 (2021), 109160 | DOI | MR | Zbl
[4] Scale matrix estimation of an elliptically symmetric distribution in high and low dimensions, J. Multivariate Anal., Volume 181 (2021), 104680 | DOI | MR | Zbl
[5] Empirical Bayes estimation of the multivariate normal covariance matrix, Ann. Stat., Volume 8 (1980) no. 3, pp. 586-597 | DOI | MR | Zbl
[6] Shrinkage estimators for large covariance matrices in multivariate real and complex normal distributions under an invariant quadratic loss, J. Multivariate Anal., Volume 100 (2009) no. 10, pp. 2237-2253 | DOI | MR | Zbl
[7] Estimation of the precision matrix of a singular Wishart distribution and its application in high-dimensional data, J. Multivariate Anal., Volume 99 (2008) no. 9, pp. 1906-1928 | DOI | MR | Zbl
[8] A well-conditioned estimator for large-dimensional covariance matrices, J. Multivariate Anal., Volume 88 (2004) no. 2, pp. 365-411 | DOI | MR | Zbl
[9] Singular Wishart and multivariate Beta distributions, Ann. Stat., Volume 31 (2003) no. 5, pp. 1537-1560 | DOI | MR | Zbl
[10] Estimation of a covariance matrix, Rietz Lecture, 39th Annual Meeting of the IMS, Atlanta, GA, 1975 (1975)
[11] Lectures on the theory of estimation of many parameters, J. Sov. Math., Volume 34 (1986) no. 1, pp. 1373-1403 | DOI | Zbl
[12] An orthogonally invariant minimax estimator of the covariance matrix of a multivariate normal population, Tsukuba J. Math., Volume 8 (1984), pp. 367-376 | DOI | MR | Zbl
[13] Estimation of a high-dimensional covariance matrix with the Stein Loss, J. Multivariate Anal., Volume 148 (2016), pp. 1-17 | DOI | MR | Zbl
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