# A diagonally weighted matrix norm between two covariance matrices

Date(s) : 25/03/2019   iCal
14 h 00 min - 15 h 00 min

The square of the Frobenius norm of a matrix \$A\$ is defined as the sum of squares of all the elements of \$A\$. An important application of the norm in statistics is when \$A\$ is the difference between a target (estimated or given) covariance matrix and a parameterized covariance matrix, whose parameters are chosen to minimize the Frobenius norm. In this article, we investigate weighting the Frobenius norm by putting more weight on the diagonal elements of \$A\$, with an application to spatial statistics. We find the spatial random effects (SRE) model that is closest, according to the the weighted Frobenius norm between covariance matrices, to a particular stationary Mat\’ern covariance model.

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