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Functional regression over irregular domains

  • Arnab Bhattacharjee

    (Heriot-Watt University)

  • Liqian Cai

    (Michigan State University)

  • Taps Maiti

    (Michigan State University)

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.

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Paper provided by Spatial Economics and Econometrics Centre, Heriot Watt University in its series SEEC Discussion Papers with number 1301.

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Date of creation: 2013
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Handle: RePEc:hwe:seecdp:1301
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  1. 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.
  2. Luc Anselin & Nancy Lozano-Gracia & Uwe Deichmann & Somik Lall, 2010. "Valuing Access to Water—A Spatial Hedonic Approach, with an Application to Bangalore, India," Spatial Economic Analysis, Taylor & Francis Journals, vol. 5(2), pages 161-179.
  3. Daniel P. McMillen, 2010. "Issues In Spatial Data Analysis," Journal of Regional Science, Wiley Blackwell, vol. 50(1), pages 119-141.
  4. 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.
  5. Rosen, Sherwin, 1974. "Hedonic Prices and Implicit Markets: Product Differentiation in Pure Competition," Journal of Political Economy, University of Chicago Press, vol. 82(1), pages 34-55, Jan.-Feb..
  6. 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.
  7. 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.
  8. 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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