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Piercesare Secchi - Politecnico di Milano Italy

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” Spatial prediction for Hilbert data”
20 February 2014 from 4:00 PM to 5:00 PM
201 Thomas Building
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When dealing with high-dimensional georeferenced data, the need of spatial prediction results in both theoretical and practical issues. The talk addresses these problems by proposing an extension of some geostatistical techniques to non-stationary functional random fields. A new theoretical framework is established to perform Universal Kriging of spatially dependent functional data belonging to a Hilbert space; moreover, estimators of the spatial mean and the spatial covariance structure are derived. The generality of the proposed approach allows to include pointwise and differential information brought by data by embedding the analysis in a proper Hilbert space, possibly other than L^2. Three environmental case studies will serve as illustration. The first deals with temperature curves embedded in L^2 while the second considers functional compositional data handled through the Aitchison geometry. In the third case study a Hilbert space approximation is exploited to make spatial predictions for data belonging to a Riemannian manifold, the space of positive definite symmetric matrices.

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