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Covariance matrix estimation under data-based loss

Author

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  • Fourdrinier, Dominique
  • Haddouche, Anis M.
  • Mezoued, Fatiha

Abstract

We consider here the problem of estimating the p×p scale matrix Σ of a multivariate linear regression model when the distribution of the observed matrix belongs to a large class of elliptically symmetric distributions. Any estimator Σˆ of Σ is assessed through the data-based loss tr(S+Σ(Σ−1Σˆ−Ip)2)where S is the sample covariance matrix and S+ is its Moore–Penrose inverse.

Suggested Citation

  • Fourdrinier, Dominique & Haddouche, Anis M. & Mezoued, Fatiha, 2021. "Covariance matrix estimation under data-based loss," Statistics & Probability Letters, Elsevier, vol. 177(C).
    • Handle: RePEc:eee:stapro:v:177:y:2021:i:c:s016771522100122x
    DOI: 10.1016/j.spl.2021.109160
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    References listed on IDEAS

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    1. Tsukuma, Hisayuki & Kubokawa, Tatsuya, 2016. "Unified improvements in estimation of a normal covariance matrix in high and low dimensions," Journal of Multivariate Analysis, Elsevier, vol. 143(C), pages 233-248.
    2. Chételat, Didier & Wells, Martin T., 2016. "Improved second order estimation in the singular multivariate normal model," Journal of Multivariate Analysis, Elsevier, vol. 147(C), pages 1-19.
    3. Tsukuma, Hisayuki, 2016. "Estimation of a high-dimensional covariance matrix with the Stein loss," Journal of Multivariate Analysis, Elsevier, vol. 148(C), pages 1-17.
    4. Dominique Fourdrinier & William Strawderman, 2015. "Robust minimax Stein estimation under invariant data-based loss for spherically and elliptically symmetric distributions," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 78(4), pages 461-484, May.
    5. Tsukuma, Hisayuki & Kubokawa, Tatsuya, 2015. "A unified approach to estimating a normal mean matrix in high and low dimensions," Journal of Multivariate Analysis, Elsevier, vol. 139(C), pages 312-328.
    6. Kubokawa, Tatsuya & Srivastava, Muni S., 2008. "Estimation of the precision matrix of a singular Wishart distribution and its application in high-dimensional data," Journal of Multivariate Analysis, Elsevier, vol. 99(9), pages 1906-1928, October.
    7. Haddouche, Anis M. & Fourdrinier, Dominique & Mezoued, Fatiha, 2021. "Scale matrix estimation of an elliptically symmetric distribution in high and low dimensions," Journal of Multivariate Analysis, Elsevier, vol. 181(C).
    8. Konno, Yoshihiko, 2009. "Shrinkage estimators for large covariance matrices in multivariate real and complex normal distributions under an invariant quadratic loss," Journal of Multivariate Analysis, Elsevier, vol. 100(10), pages 2237-2253, November.
    9. Kubokawa, T. & Srivastava, M. S., 2001. "Robust Improvement in Estimation of a Mean Matrix in an Elliptically Contoured Distribution," Journal of Multivariate Analysis, Elsevier, vol. 76(1), pages 138-152, January.
    10. Canu, Stéphane & Fourdrinier, Dominique, 2017. "Unbiased risk estimates for matrix estimation in the elliptical case," Journal of Multivariate Analysis, Elsevier, vol. 158(C), pages 60-72.
    Full references (including those not matched with items on IDEAS)

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