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Estimation of the inverse scatter matrix of an elliptically symmetric distribution

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  • Fourdrinier, Dominique
  • Mezoued, Fatiha
  • Wells, Martin T.

Abstract

We consider estimation of the inverse scatter matrices Σ−1 for high-dimensional elliptically symmetric distributions. In high-dimensional settings the sample covariance matrix S may be singular. Depending on the singularity of S, natural estimators of Σ−1 are of the form aS−1 or aS+ where a is a positive constant and S−1 and S+ are, respectively, the inverse and the Moore–Penrose inverse of S. We propose a unified estimation approach for these two cases and provide improved estimators under the quadratic loss tr(Σˆ−1−Σ−1)2. To this end, a new and general Stein–Haff identity is derived for the high-dimensional elliptically symmetric distribution setting.

Suggested Citation

  • Fourdrinier, Dominique & Mezoued, Fatiha & Wells, Martin T., 2016. "Estimation of the inverse scatter matrix of an elliptically symmetric distribution," Journal of Multivariate Analysis, Elsevier, vol. 143(C), pages 32-55.
    • Handle: RePEc:eee:jmvana:v:143:y:2016:i:c:p:32-55
    DOI: 10.1016/j.jmva.2015.08.012
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    References listed on IDEAS

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    1. 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).

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