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Testing for Local Spatial Association Based on Geographically Weighted Interpolation of Geostatistical Data with Application to PM2.5 Concentration Analysis

Author

Listed:
  • Fen-Jiao Wang

    (Department of Finance and Statistics, School of Science, Xi’an Polytechnic University, Xi’an 710048, China)

  • Chang-Lin Mei

    (Department of Finance and Statistics, School of Science, Xi’an Polytechnic University, Xi’an 710048, China)

  • Zhi Zhang

    (Department of Statistics, School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an 710049, China)

  • Qiu-Xia Xu

    (Department of Finance and Statistics, School of Science, Xi’an Polytechnic University, Xi’an 710048, China)

Abstract

Using local spatial statistics to explore local spatial association of geo-referenced data has attracted much attention. As is known, a local statistic is formulated at a particular sampling unit based on a prespecific proximity relationship and the observations in the neighborhood of this sampling unit. However, geostatistical data such as meteorological data and air pollution data are generally collected from meteorological or monitoring stations which are usually sparsely located or highly clustered over space. For such data, a local spatial statistic formulated at an isolate sampling point may be ineffective because of its distant neighbors, or the statistic is undefinable in the sub-regions where no observations are available, which limits the comprehensive exploration of local spatial association over the whole studied region. In order to overcome the predicament, a local-linear geographically weighted interpolation method is proposed in this paper to obtain the predictors of the underlying spatial process on a lattice spatial tessellation, on which a local spatial statistic can be well formulated at each interpolation point. Furthermore, the bootstrap test is suggested to identify the locations where local spatial association is significant using the interpolated-value-based local spatial statistics. Simulation with comparison to some existing interpolation and test methods is conducted to assess the performance of the proposed interpolation and the suggested test methods and a case study based on PM2.5 concentration data in Guangdong province, China, is used to demonstrate their applicability. The results show that the proposed interpolation method performs accurately in retrieving an underlying spatial process and the bootstrap test with the interpolated-value-based local statistics is powerful in identifying local patterns of spatial association.

Suggested Citation

  • Fen-Jiao Wang & Chang-Lin Mei & Zhi Zhang & Qiu-Xia Xu, 2022. "Testing for Local Spatial Association Based on Geographically Weighted Interpolation of Geostatistical Data with Application to PM2.5 Concentration Analysis," Sustainability, MDPI, vol. 14(21), pages 1-19, November.
    • Handle: RePEc:gam:jsusta:v:14:y:2022:i:21:p:14646-:d:965636
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    References listed on IDEAS

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    1. Barry Boots & Michael Tiefelsdorf, 2000. "Global and local spatial autocorrelation in bounded regular tessellations," Journal of Geographical Systems, Springer, vol. 2(4), pages 319-348, December.
    2. Bivand, Roger & Müller, Werner G. & Reder, Markus, 2009. "Power calculations for global and local Moran's," Computational Statistics & Data Analysis, Elsevier, vol. 53(8), pages 2859-2872, June.
    3. Gollini, Isabella & Lu, Binbin & Charlton, Martin & Brunsdon, Christopher & Harris, Paul, 2015. "GWmodel: An R Package for Exploring Spatial Heterogeneity Using Geographically Weighted Models," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 63(i17).
    4. Zhang, Tonglin, 2008. "Limiting distribution of the G statistics," Statistics & Probability Letters, Elsevier, vol. 78(12), pages 1656-1661, September.
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