Volume ratio, sparsity, and minimaxity under unitarily invariant norms
Volume ratio, sparsity, and minimaxity under unitarily invariant norms
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DOI：
10.1109/tit.2015.2487541
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发表时间：
2013-06
期刊：
影响因子：
--
通讯作者：
Zongming Ma;Yihong Wu
中科院分区：
文献类型：
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作者：
Zongming Ma;Yihong Wu
本文研究了高维均值和协方差阵的Minimax估计的非渐近性质。基于有限维Banach空间的凸几何，我们给出了一个统一的体积比方法，用于确定无约束均值和协方差矩阵在所有酉不变范数下的Minimax估计率.我们还建立了估计平均矩阵与组稀疏性，其中稀疏性约束引入了一个额外的长期的依赖于范数的速率完全不同的无约束的对应率的速率。
This paper presents a non-asymptotic study of the minimax estimation of high-dimensional mean and covariance matrices. Based on the convex geometry of finite-dimensional Banach spaces, we develop a unified volume ratio approach for determining minimax estimation rates of unconstrained mean and covariance matrices under all unitarily invariant norms. We also establish the rate for estimating mean matrices with group sparsity, where the sparsity constraint introduces an additional term in the rate whose dependence on the norm differs completely from the rate of the unconstrained counterpart.