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Functional regression over irregular domains

Author

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  • Arnab Bhattacharjee

    (Heriot-Watt University)

  • Liqian Cai

    (Michigan State University)

  • Taps Maiti

    (Michigan State University)

Abstract

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.

Suggested Citation

  • Arnab Bhattacharjee & Liqian Cai & Taps Maiti, 2013. "Functional regression over irregular domains," SEEC Discussion Papers 1301, Spatial Economics and Econometrics Centre, Heriot Watt University.
  • Handle: RePEc:hwe:seecdp:1301
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    References listed on IDEAS

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    5. 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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    7. 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.
    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, , vol. 30(11), pages 1905-1927, November.
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    More about this item

    Keywords

    Delaunay triangulation; Finite element; Housing markets; Spatial functional regression; Spline smoothing;

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