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Abstract:
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The estimation of covariance operators of spatio-temporal data is in many applications computationally feasible only under simplifying assumptions, such as separability of the covariance into strictly temporal and spatial factors. Powerful tests for this assumption have been proposed in the literature. However, as real world systems, such as climate data are notoriously inseparable, validating this assumption by statistical tests, seems inherently questionable.
In this talk we consider an alternative approach: By virtue of separability measures, we quantify how strongly the data's covariance operator diverges from a separable approximation. We discuss the construction of confidence intervals to localize these measures with statistical guarantees. This method provides users with a flexible tool, to weigh the computational gains of a separable model against the associated increase in bias. Our approach is based on the statistical principal of self-normalization, which makes it particularly user-friendly and robust against dependence in the data.
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