# Fréchet integration and adaptive metric selection for interpretable covariances of multivariate functional data

@article{Petersen2016FrchetIA, title={Fr{\'e}chet integration and adaptive metric selection for interpretable covariances of multivariate functional data}, author={Alexander Petersen and Hans-Georg M{\"u}ller}, journal={Biometrika}, year={2016}, volume={103}, pages={103-120} }

For multivariate functional data recorded from a sample of subjects on a common domain, one is often interested in the covariance between pairs of the component functions, extending the notion of a covariance matrix for multivariate data to the functional case. A straightforward approach is to integrate the pointwise covariance matrices over the functional time domain. We generalize this approach by defining the Frechet integral, which depends on the metric chosen for the space of covariance…

## 16 Citations

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This work introduces novel statistical techniques to analyse geolocalised speech recordings and to explore the spatial variation of pronunciations continuously over the region of interest, as opposed to traditional isoglosses, which provide a discrete partition of the region.

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