000197061 001__ 197061
000197061 005__ 20190316235843.0
000197061 0247_ $$2doi$$a10.1137/130925426
000197061 037__ $$aARTICLE
000197061 245__ $$aMixed Finite Elements for spatial regression with PDE penalization
000197061 269__ $$a2014
000197061 260__ $$c2014
000197061 336__ $$aJournal Articles
000197061 520__ $$aWe study a class of models at the interface between statistics and numerical analysis. Specifically, we consider nonparametric regression models for the estimation of spatial fields from pointwise and noisy observations, which account for problem-specific prior information, described in terms of a partial differential equation governing the phenomenon under study. The prior information is incorporated in the model via a roughness term using a penalized regression framework. We prove the well-posedness of the estimation problem, and we resort to a mixed equal order finite element method for its discretization. Moreover, we prove the well-posedness and the optimal convergence rate of the proposed discretization method. Finally the smoothing technique is extended to the case of areal data, particularly interesting in many applications.
000197061 6531_ $$amixed Finite Element method
000197061 6531_ $$afourth order problems
000197061 6531_ $$anon-parametric regression
000197061 6531_ $$asmoothing
000197061 700__ $$aAzzimonti, Laura
000197061 700__ $$0241873$$g118353$$aNobile, Fabio
000197061 700__ $$aSangalli, Laura M.
000197061 700__ $$aSecchi, Piercesare
000197061 773__ $$j2$$tSIAM/ASA Journal on Uncertainty Quantification$$k1$$q305--335
000197061 8564_ $$uhttps://infoscience.epfl.ch/record/197061/files/2014_Azzimonti_Nobile_Sangalli_Secchi_JUQ_Mixed.pdf$$zn/a$$s629396$$yn/a
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000197061 917Z8 $$x118353
000197061 917Z8 $$x118353
000197061 917Z8 $$x118353
000197061 917Z8 $$x118353
000197061 937__ $$aEPFL-ARTICLE-197061
000197061 973__ $$rREVIEWED$$sPUBLISHED$$aEPFL
000197061 980__ $$aARTICLE