This work addresses large dimensional covariance matrix estimation with unknown mean. The empirical covariance estimator fails when dimension and number of samples are proportional and tend to infinity, settings known as Kolmogorov asymptotics. When the mean is known, Ledoit and Wolf (2004) proposed a linear shrinkage estimator and proved its convergence under those asymptotics. To the best of our knowledge, no formal proof has been proposed when the mean is unknown. To address this issue, we propose a new estimator and prove its quadratic convergence under the Ledoit and Wolf assumptions. Finally, we show empirically that it outperforms other standard estimators.

翻译：本文研究在未知均值情况下的大维协方差矩阵估计问题。在维度和样本量成正比且趋向于无穷大的 Kolmogorov渐进情况下，经验协方差估计器不再适用。当均值已知时，Ledoit和Wolf (2004) 提出了线性缩减估计器并证明其在这些渐进情况下的收敛性。据我们所知，在均值未知情况下尚未提出正式证明。为解决这个问题，我们提出了一种新的估计器，并在Ledoit和Wolf的假设下证明了其二阶收敛性。最后，我们通过实验表明该估计器优于其他标准估计器。