We consider the problem of estimating the covariance matrix of a random vector by observing i.i.d samples and each entry of the sampled vector is missed with probability $p$. Under the standard $L_4-L_2$ moment equivalence assumption, we construct the first estimator that simultaneously achieves optimality with respect to the parameter $p$ and it recovers the optimal convergence rate for the classical covariance estimation problem when $p=1$

翻译：我们考虑通过观测独立同分布样本来估计随机向量协方差矩阵的问题，其中采样向量的每个条目以概率$p$缺失。在标准$L_4-L_2$矩等价假设下，我们构建了首个同时实现关于参数$p$的统计最优性，并在$p=1$时恢复经典协方差估计问题最优收敛速率的估计量。