Robust improvement in estimation of a covariance matrix in an elliptically contoured distribution

DOI10.1214/aos/1018031209zbMath0942.62063OpenAlexW1570750275MaRDI QIDQ1970481

Tatsuya Kubokawa, Muni S. Srivastava

Publication date: 7 June 2000

Published in: The Annals of Statistics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1214/aos/1018031209

zbMATH Keywords

covariance matrixelliptically contoured distributionrobustness of improvementshrinkage estimationmultivariate linear model

Mathematics Subject Classification ID

Estimation in multivariate analysis (62H12) Linear regression; mixed models (62J05) Statistical decision theory (62C99)

Related Items (20)

Estimation of a high-dimensional covariance matrix with the Stein loss ⋮ On improved loss estimation for shrinkage estimators ⋮ Scale matrix estimation of an elliptically symmetric distribution in high and low dimensions ⋮ Invariance properties of the likelihood ratio for covariance matrix estimation in some complex elliptically contoured distributions ⋮ Estimation of the inverse scatter matrix of an elliptically symmetric distribution ⋮ Improved estimation of a covariance matrix in an elliptically contoured matrix distribution ⋮ On the non existence of unbiased estimators of risk for spherically symmetric distributions ⋮ On completeness of the general linear model with spherically symmetric errors ⋮ Improving on the sample covariance matrix for a complex elliptically contoured distribution ⋮ Covariance matrix estimation under data-based loss ⋮ Estimation of the precision matrix of a singular Wishart distribution and its application in high-dimensional data ⋮ Robust improvement in estimation of a mean matrix in an elliptically contoured distribution ⋮ Estimation of a scale parameter in mixture models with unknown location ⋮ Alternative estimators of the common regression matrix in two GMANOVA models under weighted quadratic losses ⋮ An asymptotic expansion of Wishart distribution when the population eigenvalues are infinitely dispersed ⋮ Stein–Haff identity for the exponential family ⋮ Multivariate elliptically contoured autoregressive process ⋮ An identity for multivariate elliptically contoured matrix distribution ⋮ Robust minimax Stein estimation under invariant data-based loss for spherically and elliptically symmetric distributions ⋮ The Stein effect for Fréchet means

Cites Work

• An orthogonally invariant minimax estimator of the covariance matrix of a multivariate normal population
• Estimation of a covariance matrix under Stein's loss
• Stein estimation under elliptical distributions
• Robust shrinkage estimators of the location parameter for elliptically symmetric distributions
• An identity for the Wishart distribution with applications
• Inadmissibility of non-order-preserving orthogonally invariant estimators of the covariance matrix in the case of Stein's loss
• Estimation of a covariance matrix using the reference prior
• Minimax estimators in the normal MANOVA model
• Explicit bounds and heuristics on class numbers in hyperelliptic function fields
• Reference prior bayes estimator for bivariate normal covariance matrix with risk comparison
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