A0284
Title: Spatial regression with PDE penalization: Consistency of the estimator
Authors: Eleonora Arnone - University of Turin (Italy) [presenting]
Alois Kneip - University of Bonn (Germany)
Fabio Nobile - Ecole Polytechnique Federale de Lausanne (Switzerland)
Laura Sangalli - Politecnico di Milano (Italy)
Abstract: The consistency of the estimator in Spatial Regression with Partial Differential Equation penalization method (SR-PDE) is studied. SR-PDE is a technique for the estimation of a spatial dependent field over a two-dimensional complex domain from pointwise noisy observations when prior information on the field is available in form of a PDE. The consistency is studied both for the estimator in the infinite dimensional setting and for the discrete estimator obtained with finite elements method. Bias and variance of the estimator are analyzed with respect to the sample size and the value of the smoothing parameter. It is shown that optimal rates of convergence can be reached for the mean squared error in the $L^2$ and discrete norm when the number of observations goes to infinity. Simulation studies to verify the convergence rates are performed in a simple setting.
