Functional regression over irregular domains: Variation in the shadow price of living space

Hedonic house price models need to account for spatial heterogeneity - the variation in the functional surface of shadow prices. In this context, the complexity of spatial domains raises issues for the traditional spatial smoothing methods. Specifically, discontinuities in the spatial surface need to be accounted for, including for example, irregular boundaries, peninsulas and interior holes. Motivated by an application to housing markets, we develop a method for estimating the functional surface of a regression coefficient that varies over such a complex spatial domain. Spatially varying coefficients for a specific regressor are estimated by a combination of three spline smoothing problems, the penalties of which are based on a partial differential operator integrated only over the problem domain by using finite element analysis. The effect of additional regressors is also allowed. We verify finite sample performance using a simulation study. As an illustration, the method is applied to data from the Aveiro-Ílhavo urban housing market in Portugal.