Functional regression over irregular domains

We develop a method for estimating the functional surface of a regression coefficient that varies over a complex spatial domain with irregular boundaries, peninsulas and interior holes. The method is motivated by, and applied to, data on housing markets, where the central object of inference is estimation of spatially varying effects of living space on house prices. For this purpose, we extend a method of spline smoothing over an irregular domain to the functional regression model. Spatially varying coefficients for a specific regressor are estimated by a combination of three smoothing problems, allowing for additional regressors with spatially fixed coefficients. The estimates adapt well to the irregular and complex spatial domain. Implicit prices for living space vary spatially, being high in the city centre and other desirable locations, and declining towards the periphery along gradients determined by major roads.