Separable covariance structure identification for doubly multivariate data
[ 1 ] Instytut Matematyki, Wydział Automatyki, Robotyki i Elektrotechniki, Politechnika Poznańska | [ P ] employee
2021
chapter in monograph
english
- doubly multivariate data
- entropy loss function
- Frobenius norm
- covariance structure indentification
- separability
EN The aim of this paper is to present two methods for the identification of separable covariance structures with both components unstructured, or with one component additionally structured as compound symmetry or first-order autoregression, for doubly multivariate data. As measures of discrepancy between an unstructured covariance matrix and the structured one, the Frobenius norm and the entropy loss function are used. The minimum of each discrepancy function is presented, and then simulation studies are performed to verify whether the considered discrepancy functions recognize the true covariance structure properly. An interpretation of the presented approach using a real data example is also given. This paper is mainly an overview of the papers by van Loan and Pitsianis (1992), Filipiak and Klein (2018), Filipiak et al. (2018), Filipiak et al. (2021).
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