Multi-target linear shrinkage is an extension of the standard single-target linear shrinkage for covariance estimation. We combine several constant matrices - the targets - with the sample covariance matrix. We derive the oracle and a \textit{bona fide} multi-target linear shrinkage estimator with exact and empirical mean. In both settings, we proved its convergence towards the oracle under Kolmogorov asymptotics. Finally, we show empirically that it outperforms other standard estimators in various situations.

翻译：多目标线性收缩是标准单目标线性收缩在协方差估计中的扩展。我们将样本协方差矩阵与多个常数矩阵（即目标矩阵）相结合。推导出具有精确均值和经验均值的理想及实际多目标线性收缩估计器。在这两种设定下，我们证明了其在柯尔莫哥洛夫渐近条件下向理想估计器的收敛性。最后，我们通过实证表明，该估计器在多种情境下优于其他标准估计器。