We consider the problem of analyzing spatially distributed data characterized by spatial anisotropy. Following a functional data analysis approach, we propose a method based on regression with partial differential regularization, where the differential operator in the regularizing term is anisotropic and is derived from data. We show that the method correctly identifies the direction and intensity of anisotropy and returns an accurate estimate of the spatial field. The method compares favorably to both isotropic and anisotropic kriging, as tested in simulation studies under various scenarios. The method is then applied to the analysis of Switzerland rainfall data.

Modeling spatial anisotropy via regression with partial differential regularization

Bernardi, Mara S.;Sangalli, Laura M.
2018-01-01

Abstract

We consider the problem of analyzing spatially distributed data characterized by spatial anisotropy. Following a functional data analysis approach, we propose a method based on regression with partial differential regularization, where the differential operator in the regularizing term is anisotropic and is derived from data. We show that the method correctly identifies the direction and intensity of anisotropy and returns an accurate estimate of the spatial field. The method compares favorably to both isotropic and anisotropic kriging, as tested in simulation studies under various scenarios. The method is then applied to the analysis of Switzerland rainfall data.
Finite elements; Functional data analysis; Parameter cascading; Penalized regression; Statistics and Probability; Numerical Analysis; Statistics, Probability and Uncertainty
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11311/1059541
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