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A theoretical study of Stein's covariance estimator

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  • Bala Rajaratnam
  • Dario Vincenzi

Abstract

Stein proposed an estimator to address the poor performance of the sample covariance matrix for samples of small size. The estimator does not impose sparsity conditions and uses an isotonizing algorithm to preserve the order of the sample eigenvalues. Despite its superior numerical performance, its theoretical properties are not well understood. We demonstrate that Stein's covariance estimator gives modest risk reductions when it is not isotonized, and when it is isotonized the risk reductions are significant. Three broad regimes of the estimator's behaviour are identified.

Suggested Citation

  • Bala Rajaratnam & Dario Vincenzi, 2016. "A theoretical study of Stein's covariance estimator," Biometrika, Biometrika Trust, vol. 103(3), pages 653-666.
  • Handle: RePEc:oup:biomet:v:103:y:2016:i:3:p:653-666.
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    File URL: http://hdl.handle.net/10.1093/biomet/asw030
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    1. Schäfer Juliane & Strimmer Korbinian, 2005. "A Shrinkage Approach to Large-Scale Covariance Matrix Estimation and Implications for Functional Genomics," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 4(1), pages 1-32, November.
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    Cited by:

    1. Olivier Ledoit & Michael Wolf, 2017. "Analytical nonlinear shrinkage of large-dimensional covariance matrices," ECON - Working Papers 264, Department of Economics - University of Zurich, revised Nov 2018.
    2. Olivier Ledoit & Michael Wolf, 2019. "Quadratic shrinkage for large covariance matrices," ECON - Working Papers 335, Department of Economics - University of Zurich, revised Dec 2020.

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