We give a new algorithm for the estimation of the cross-covariance matrix $\mathbb{E} XY'$ of two large dimensional signals $X\in\mathbb{R}^n$, $Y\in \mathbb{R}^p$ in the context where the number $T$ of observations of the pair $(X,Y)$ is large but $n/T$ and $p/T$ are not supposed to be small. In the asymptotic regime where $n,p,T$ are large, with high probability, this algorithm is optimal for the Frobenius norm among rotationally invariant estimators, i.e. estimators derived from the empirical estimator by cleaning the singular values, while letting singular vectors unchanged.

翻译：我们给出了一种新的算法来估算交叉变量矩阵 $\ mathbb{E} XY $,用于估算两个大维信号 $X\ in\ mathbb{R ⁇ n$, $Y\in\ mathb{R ⁇ p$, 在对(X, Y) 美元观测的美元数额很大但n/ t美元/ t美元和$p/ T美元的数值不应该很小的情况下。 在无药可依的体系中, $n, p, T$是大的, 概率很高的, 这个算法对于Frobenius 规范来说是最佳的, 由旋转不定的估量者, 即通过清理单值而允许单向矢量不变, 从实验估量中得出的估量者。