Generalized Spatial Regression with Differential Regularization

Generalized Spatial Regression with Differential Regularization
Thursday 5th May 2016
Wilhelm, M.; Sangalli, L.M.
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We aim at analyzing geostatistical and areal data observed over irregularly shaped spatial domains and having a distribution within the exponential family. We propose a generalized additive model that allows to account for spatially-varying covariate information. The model is fitted by maximizing a penalized log-likelihood function, with a roughness penalty term that involves a differential quantity of the spatial field, computed over the domain of interest. Efficient estimation of the spatial field is achieved resorting to the finite element method, which provides a basis for piecewise polynomial surfaces. The proposed model is illustrated by an application to the study of criminality in the city of Portland, Oregon, USA.
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Journal of Statistical Computation and Simulation, 2016, 86 (13), 2497-2518