A diagonally weighted matrix norm between two covariance matrices
Date(s) : 25/03/2019 iCal
14h00 - 15h00
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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