The Review of Economics and Statistics Vol. 106 No. 4 2024
A Canonical Representation of Block Matrices with Applications to Covariance and Correlation Matrices
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.
- DOI
- 10.1162/rest_a_01258
- Volume
- 106
- Issue
- 4
- Pages
- 1099-1113
- Language
- en
- Sources
- bibtex:phds-export.bib openalex crossref