A Canonical Representation of Block Matrices with Applications to Covariance and Correlation Matrices
提出分块矩阵的规范表示，简化了行列式、逆、幂、对数及指数等运算，特别适用于协方差和相关矩阵的高斯似然估计，并用大面板资产收益数据验证。
Abstract 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 model and regularize large covariance/correlation matrices, test block structures in matrices, and estimate regressions with many variables.