Spatial regression models over two-dimensional manifolds

Spatial regression models over two-dimensional manifolds
Thursday 13th December 2012
Ettinger, B., Perotto, S.; Sangalli, L.M.
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We propose a regression model for data spatially distributed over nonplanar two-dimensional Riemannian manifolds. The model is a generalized additive model with a roughness penalty term involving a suitable differential operator computed over the non-planar domain. Thanks to a semi-parametric framework, the model allows for inclusion of space-varying covariate information. We show that the estimation problem can be solved first by conformally mapping the non-planar domain to a planar domain and then by applying existing models for penalized spatial regression over planar domains, appropriately modified to account for the domain deformation. The flattening map and the estimation problem are both computed by resorting to a finite element approach. The estimators are linear in the observed data values and classical inferential tools are derived. The application driving this research is the study of hemodynamic forces on the wall of an internal carotid artery affected by an aneurysm.