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    Penalized Local Polynomial Regression for Spatial Data

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    Type
    Article
    Authors
    Wang, Wu
    Sun, Ying cc
    KAUST Department
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Statistics Program
    Date
    2019-04-25
    Permanent link to this record
    http://hdl.handle.net/10754/632545
    
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    Abstract
    When performing spatial regression analysis in environmental data applications, spatial heterogeneity in the regression coefficients is often observed. Spatially varying coefficient models, including geographically weighted regression and spline models, are standard tools for quantifying such heterogeneity. In this paper, we propose a spatially varying coefficient model that represents the spatially varying parameters as a mixture of local polynomials at selected locations. The local polynomial parameters have attractive interpretations, indicating various types of spatial heterogeneity. Instead of estimating the spatially varying regression coefficients directly, we develop a penalized least squares regression procedure for the local polynomial parameter estimation, which both shrinks the parameter estimation and penalizes the differences among parameters that are associated with neighboring locations. We develop confidence intervals for the varying regression coefficients and prediction intervals for the response. We apply the proposed method to characterize the spatially varying association between particulate matter concentrations (PM2.5 ) and pollutant gases related to the secondary aerosol formulation in China. The identified regression coefficients show distinct spatial patterns for nitrogen dioxide, sulfur dioxide, and carbon monoxide during different seasons. This article is protected by copyright. All rights reserved.
    Citation
    Wang W, Sun Y (2019) Penalized Local Polynomial Regression for Spatial Data. Biometrics. Available: http://dx.doi.org/10.1111/biom.13077.
    Sponsors
    We thank the associate editor and a referee for their help in improving the paper. This research was supported by funding from King Abdullah University of Science and Technology (KAUST).
    Publisher
    Wiley
    Journal
    Biometrics
    DOI
    10.1111/biom.13077
    Additional Links
    https://onlinelibrary.wiley.com/doi/abs/10.1111/biom.13077
    ae974a485f413a2113503eed53cd6c53
    10.1111/biom.13077
    Scopus Count
    Collections
    Articles; Statistics Program; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

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