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Multivariate functional random fields: prediction and optimal sampling

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Abstract

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 México city.

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Acknowledgments

The authors are grateful to the positive comments made by the reviewers and the Associate Editor that have improved the quality of the manuscript.

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Correspondence to M. Bohorquez.

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Bohorquez, M., Giraldo, R. & Mateu, J. Multivariate functional random fields: prediction and optimal sampling. Stoch Environ Res Risk Assess 31, 53–70 (2017). https://doi.org/10.1007/s00477-016-1266-y

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  • DOI: https://doi.org/10.1007/s00477-016-1266-y

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