Spatially varying coefficient models are a classical tool to explore the spatial nonstationarity of a regression relationship for spatial data. In this paper, we study the estimation and inference in spatially varying coefficient models for data distributed over complex domains. We use bivariate splines over triangulations to represent the coefficient functions. The estimators of the coefficient functions are consistent, and rates of convergence of the proposed estimators are established. A penalized bivariate spline estimation method is also introduced, in which a roughness penalty is incorporated to balance the goodness of fit and smoothness. In addition, we propose hypothesis tests to examine if the coefficient function is really varying over space or admits a certain parametric form. The proposed method is much more computationally efficient than the well-known geographically weighted regression technique and thus usable for analyzing massive data sets. The performances of the estimators and the proposed tests are evaluated by simulation experiments. An environmental data example is used to illustrate the application of the proposed method.
Mu, Jingru; Wang, Guannan; and Wang, Li, Estimation and inference in spatially varying coefficient models (2018). Environmetrics, 29(1).