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Title: A canonical representation of block matrices with applications to covariance and correlation matrices Authors:  Ilya Archakov - University of Vienna (Austria) [presenting]
Peter Hansen - University of North Carolina (United States)
Abstract: A canonical representation for block matrices is obtained. 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 matrices and block correlation matrices, where the evaluation of the Gaussian log-likelihood and the estimation is greatly simplified. We illustrate this with an empirical application using a large panel of daily asset returns. Moreover, the representation paves new ways to regularize large covariance/correlation matrices and to test block structures in matrices.