处理奇异样本协方差阵的新方法
New Methods for Handling Singular Sample Covariance Matrices
摘要：
在多元统计学、无线通信、信号处理、生物学、学习理论和金融学等领域中，从不足的数据量估计协方差阵是最常见的问题之一。在Marzetta、Tucci和Simon的联合工作中，提出了一种处理奇异协方差阵的新方法。其主要思想是使用降维结合平均在Stiefel流形。在本文中，我们继续这项研究，我们认为一些新的方法来解决这个问题。其中一种方法被称为Ewens估计器，并使用关于Ewens测量的所有置换矩阵上的样本协方差阵的随机化。用于解决这个问题的技术是广泛的，从随机矩阵理论到组合学。
英文摘要：
The estimation of a covariance matrix from an insufficient amount of data is one of the most common problems in fields as diverse as multivariate statistics, wireless communications, signal processing, biology, learning theory and finance. In a joint work of Marzetta, Tucci and Simon, a new approach to handle singular covariance matrices was suggested. The main idea was to use dimensionality reduction in conjunction with an average over the Stiefel manifold. In this paper we continue with this research and we consider some new approaches to solve this problem. One of the methods is called the Ewens estimator and uses a randomization of the sample covariance matrix over all the permutation matrices with respect to the Ewens measure. The techniques used to attack this problem are broad and run from random matrix theory to combinatorics.
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