Multivariate functional random fields: prediction and optimal sampling

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This paper develops spatial prediction of a functional variable at unsampled sites, using functional covariates, that is, we present a functional cokriging method. We show that through the representation of each function in terms of its empirical functional principal components, the functional cokriging only depends on the auto-covariance and cross-covariance of the associated scores vectors, which are scalar random fields. In addition, we propose the methodology to find optimal sampling designs in this context. The proposal is applied to the network of air quality in Mexico city.