论文标题
块矩阵的规范表示，并应用于协方差和相关矩阵
A Canonical Representation of Block Matrices with Applications to Covariance and Correlation Matrices
论文作者
论文摘要
我们获得了块矩阵的规范表示。表示形式促进了块矩阵的确定因素，矩阵逆和其他功率的简单计算，以及矩阵对数和矩阵指数。这些结果对于块协方差和块相关矩阵特别有用，在该矩阵中，对高斯对数似然性和估计的评估得到了极大的简化。我们使用大量每日资产回报板的经验应用来说明这一点。此外，表示形式铺平了新的方法，以使大量协方差/相关矩阵，矩阵中的测试块结构以及许多变量的回归进行估算。
We obtain a canonical representation for block matrices. The representation facilitates simple computation of the determinant, the matrix inverse, and other powers of a block matrix, as well as the matrix logarithm and the matrix exponential. These results are particularly useful for block covariance and block correlation matrices, where evaluation of the Gaussian log-likelihood and estimation are greatly simplified. We illustrate this with an empirical application using a large panel of daily asset returns. Moreover, the representation paves new ways to regularizing large covariance/correlation matrices, test block structures in matrices, and estimate regressions with many variables.
