分块矩阵的标准表示及其在协方差和相关矩阵中的应用
A Canonical Representation of Block Matrices with Applications to Covariance and Correlation Matrices
摘要：
我们得到了分块矩阵的一个标准表示。该表示便于简单计算行列式、矩阵逆和分块矩阵的其他幂，以及矩阵对数和矩阵指数。这些结果是特别有用的块协方差和块相关矩阵，其中高斯对数似然估计的评估大大简化。我们说明了这一点的实证应用，使用一个大面板的每日资产收益率。此外，表示铺平了新的方法来正则化大型协方差/相关矩阵，矩阵中的测试块结构，并估计回归与许多变量。
英文摘要：
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.
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