Abstract
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 [18], Filipiak and Klein [8], Filipiak et al. [10], Filipiak et al. [12].
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Acknowledgements
The authors thank Stefan Banach International Mathematical Center, Institute of Mathematics of the Polish Academy of Sciences, Warsaw, for providing the opportunity and support for this paper. This research is partially supported by Scientific Activities No. 04/43/SBAD/0115 (Katarzyna Filipiak) and by the Slovak Research and Development Agency under contract no. APVV-17-0568 and VEGA MŠ SR 1/0311/18 (Daniel Klein).
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Filipiak, K., Klein, D., Mokrzycka, M. (2021). Separable Covariance Structure Identification for Doubly Multivariate Data. In: Filipiak, K., Markiewicz, A., von Rosen, D. (eds) Multivariate, Multilinear and Mixed Linear Models. Contributions to Statistics. Springer, Cham. https://doi.org/10.1007/978-3-030-75494-5_5
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