Semiparametric Regression for Spatial Anisotropic Data With Unknown Forcing Terms in the Prior PDE

This paper introduces a new semiparametric spatial regression model with unknown forcing terms (SSRUT) in the prior information of the nonparametric function for spatial anisotropic data. The estimators are obtained by the proposed penalized least squares method which incorporates partial differential equation (PDE) penalization with mixed finite elements. In particular, the unknown coefficient functions in PDE which capture the spatial anisotropy, are chosen by our developed penalized spatial local least squares method. The corresponding implementation procedure is also developed. Extensive simulations and a real data analysis are conducted to validate the effectiveness of the proposed estimation approach.