Testing the covariance structure of multivariate random fields

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Spiked separable covariance matrices and principal components (2019, background): “High-dimensional data obtained at space-time points has been increasingly employed in various scientific fields, such as geophysical and environmental sciences [32, 36], wireless communications [28, 52, 54], medical imaging [49] and financial economics [41, 42, 59].”
Non‐stationary Cross‐Covariance Models for Multivariate Processes on a Globe (2011, background): “Jun & Stein (2007) proposed an approach to produce non-stationary covariance models for a univariate process on a globe to capture space-time asymmetry, which is commonly found in environmental data (Gneiting, 2002; Jun & Stein, 2004; Li et al., 2008).”
Spatio-Temporal Covariance and Cross-Covariance Functions of the Great Circle Distance on a Sphere (2016, methodology): “The choice of functions from Tables S1 and S2 of the OS can be guided empirically by testing procedures of the structure of space-time covariance functions as developed by Li, Genton, and Sherman (2007); extensions to the structure of cross-covariance functions are in Li, Genton, and Sherman (2008).”
Cross-covariance functions for multivariate random fields based on latent dimensions (2010, methodology): “Li et al. (2008) tested the structure of the cross-covariance functions of this dataset and concluded that it was highly variable nonseparable and asymmetric, hence that a linear model of coregionalization was not appropriate.”