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Title: Prediction and optimal sampling for spatial multivariate functional random fields Authors:  Martha Bohorquez - Universidad Nacional de Colombia (Colombia) [presenting]
Ramon Giraldo - Universidad Nacional de Colombia (Colombia)
Jorge Mateu - University Jaume I (Spain)
Abstract: The framework of optimal sampling designs is extended to the spatial prediction of univariate and multivariate functional data. In both cases, we derive unbiased predictors and their variances. In the univariate case, we propose to use a simple cokriging predictor with the scalar random fields resulting from the scores associated to the representation of the functional data with the empirical functional principal components. In the multivariate case, we develop 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 score vectors, which are scalar random fields. Design criteria are given for all predictors derived in this thesis. The methodologies are applied to the networks of air quality of Bogota and Mexico.