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Covariance matrix estimation via bilinear shrinkage regularization
  • Bin Zhang,
  • Shoucheng Yuan
Bin Zhang
Guangxi Normal University

Corresponding Author:[email protected]

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Shoucheng Yuan
Pu'er University
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The problem of estimating a covariance matrix plays crucial in signal processing and other related fields. This paper proposes a novel bilinear shrinkage estimation by simultaneously regularizing the sample mean and the SCM via the linear shrinkage technique. Through a one-one mapping of the weight parameters, the bilinear shrinkage estimation can be expressed as a generalization version of the well-known linear shrinkage estimation. Available covariance matrix estimators are developed by parametric and nonparametric methods for different target matrices. In our numerical simulations, the bilinear shrinkage estimators can reach lower Frobenius losses compared with the existing linear shrinkage estimators. Moreover, the proposed covariance matrix estimators can work well in application to large array signal processing.