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Empirical Bayesian estimation of normal variances and covariances

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  • Champion, Colin J.

Abstract

This paper derives and evaluates an algorithm for estimating normal covariances. A particular concern is the performance of the estimator when the dimension of the space exceeds the number of observations. The algorithm is simple, tolerably well founded, and seems to be more accurate for its purpose than the alternatives. Other topics discussed are the joint estimation of variances in one and many dimensions; the loss function appropriate to a variance estimator; and its connection with a certain Bayesian prescription.

Suggested Citation

  • Champion, Colin J., 2003. "Empirical Bayesian estimation of normal variances and covariances," Journal of Multivariate Analysis, Elsevier, vol. 87(1), pages 60-79, October.
    • Handle: RePEc:eee:jmvana:v:87:y:2003:i:1:p:60-79
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    References listed on IDEAS

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    1. Michael J. Daniels & Robert E. Kass, 2001. "Shrinkage Estimators for Covariance Matrices," Biometrics, The International Biometric Society, vol. 57(4), pages 1173-1184, December.
    2. Ghosh M. & Sinha B. K., 1987. "Inadmissibility Of The Best Equivariant Estimators Of The Variance-Covariance Matrix, The Precision Matrix, And The Generalized Variance Under Entropy Loss," Statistics & Risk Modeling, De Gruyter, vol. 5(3-4), pages 201-228, April.
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    Cited by:

    1. Yeil Kwon & Zhigen Zhao, 2023. "On F-modelling-based empirical Bayes estimation of variances," Biometrika, Biometrika Trust, vol. 110(1), pages 69-81.
    2. Howlett, P.G. & Torokhti, A. & Pearce, C.E.M., 2007. "Optimal multilinear estimation of a random vector under constraints of causality and limited memory," Computational Statistics & Data Analysis, Elsevier, vol. 52(2), pages 869-878, October.

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