ADAPTIVE COVARIANCE MATRIX ESTIMATION THROUGH BLOCK THRESHOLDING
ADAPTIVE COVARIANCE MATRIX ESTIMATION THROUGH BLOCK THRESHOLDING
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DOI：
10.1214/12-aos999
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发表时间：
2012-08-01
影响因子：
4.5
通讯作者：
Yuan, Ming
中科院分区：
文献类型：
--
作者：
Cai, Tony;Yuan, Ming
大的协方差矩阵的估计引起了相当多的关注，理论上的重点，到目前为止，主要是在一个固定的参数空间上发展的极大极小理论。在本文中，我们考虑自适应协方差矩阵估计的目标是建立一个单一的程序，这是最小最大率同时在每个参数空间在一个大的集合。提出了一种完全数据驱动的块阈值估计器。估计器的构造是通过仔细划分样本协方差矩阵成块，然后同时估计块中的条目通过阈值。估计是最佳率自适应在很宽的范围内的可带协方差矩阵。仿真研究表明，块阈值估计器在数值上表现良好。本文中开发的一些技术工具也可以是独立的兴趣。
Estimation of large covariance matrices has drawn considerable recent attention, and the theoretical focus so far has mainly been on developing a minimax theory over a fixed parameter space. In this paper, we consider adaptive covariance matrix estimation where the goal is to construct a single procedure which is minimax rate optimal simultaneously over each parameter space in a large collection. A fully data-driven block thresholding estimator is proposed. The estimator is constructed by carefully dividing the sample covariance matrix into blocks and then simultaneously estimating the entries in a block by thresholding. The estimator is shown to be optimally rate adaptive over a wide range of bandable covariance matrices. A simulation study is carried out and shows that the block thresholding estimator performs well numerically. Some of the technical tools developed in this paper can also be of independent interest.