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A diagonally weighted matrix norm between two covariance matrices

journal contribution
posted on 2024-11-16, 04:50 authored by Noel CressieNoel Cressie, Cecile Hardouin
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 weighted Frobenius norm between covariance matrices, to a particular stationary Matérn covariance model.

Funding

Spatio-Temporal Statistics and its Application to Remote Sensing

Australian Research Council

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Citation

Cressie, N. & Hardouin, C. (2019). A diagonally weighted matrix norm between two covariance matrices. Spatial Statistics, 29 316-328.

Journal title

Spatial Statistics

Volume

29

Pagination

316-328

Language

English

RIS ID

133043

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