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.
|Date of creation:||2013|
|Date of revision:|
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- Daniel P. McMillen & Christian L. Redfearn, 2010. "Estimation And Hypothesis Testing For Nonparametric Hedonic House Price Functions," Journal of Regional Science, Wiley Blackwell, vol. 50(3), pages 712-733.
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- A S Fotheringham & M E Charlton & C Brunsdon, 1998. "Geographically weighted regression: a natural evolution of the expansion method for spatial data analysis," Environment and Planning A, Pion Ltd, London, vol. 30(11), pages 1905-1927, November.
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- Simon N. Wood & Mark V. Bravington & Sharon L. Hedley, 2008. "Soap film smoothing," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(5), pages 931-955.
- Daniel P. McMillen, 2010. "Issues In Spatial Data Analysis," Journal of Regional Science, Wiley Blackwell, vol. 50(1), pages 119-141.
- David O'Donnell & Alastair Rushworth & Adrian W. Bowman & E. Marian Scott & Mark Hallard, 2014. "Flexible regression models over river networks," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 63(1), pages 47-63, 01.
- Haonan Wang & M. Giovanna Ranalli, 2007. "Low-Rank Smoothing Splines on Complicated Domains," Biometrics, The International Biometric Society, vol. 63(1), pages 209-217, 03.
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