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Use of Correlated Data for Nonparametric Prediction of a Spatial Target Variable

Author

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  • Pilar García-Soidán

    (Department of Statistics and Operations Research, University of Vigo, Campus A Xunqueira, 36005 Pontevedra, Spain)

  • Tomás R. Cotos-Yáñez

    (Department of Statistics and Operations Research, University of Vigo, Campus As Lagoas, 32004 Ourense, Spain)

Abstract

The kriging methodology can be applied to predict the value of a spatial variable at an unsampled location, from the available spatial data. Furthermore, additional information from secondary variables, correlated with the target one, can be included in the resulting predictor by using the cokriging techniques. The latter procedures require a previous specification of the multivariate dependence structure, difficult to characterize in practice in an appropriate way. To simplify this task, the current work introduces a nonparametric kernel approach for prediction, which satisfies good properties, such as asymptotic unbiasedness or the convergence to zero of the mean squared prediction error. The selection of the bandwidth parameters involved is also addressed, as well as the estimation of the remaining unknown terms in the kernel predictor. The performance of the new methodology is illustrated through numerical studies with simulated data, carried out in different scenarios. In addition, the proposed nonparametric approach is applied to predict the concentrations of a pollutant that represents a risk to human health, the cadmium, in the floodplain of the Meuse river (Netherlands), by incorporating the lead level as an auxiliary variable.

Suggested Citation

  • Pilar García-Soidán & Tomás R. Cotos-Yáñez, 2020. "Use of Correlated Data for Nonparametric Prediction of a Spatial Target Variable," Mathematics, MDPI, vol. 8(11), pages 1-20, November.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:11:p:2077-:d:448422
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    References listed on IDEAS

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    1. Raquel Menezes & Pilar García-Soidán & Célia Ferreira, 2010. "Nonparametric spatial prediction under stochastic sampling design," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 22(3), pages 363-377.
    2. Wenceslao González‐Manteiga & Rosa M. Crujeiras & Mario Francisco‐Fernández & Alejandro Quintela‐del‐Río & Rubén Fernández‐Casal, 2012. "Nonparametric methods for spatial regression. An application to seismic events," Environmetrics, John Wiley & Sons, Ltd., vol. 23(1), pages 85-93, February.
    3. Ramón Giraldo & Luis Herrera & Víctor Leiva, 2020. "Cokriging Prediction Using as Secondary Variable a Functional Random Field with Application in Environmental Pollution," Mathematics, MDPI, vol. 8(8), pages 1-13, August.
    4. Kleiber, William & Nychka, Douglas, 2012. "Nonstationary modeling for multivariate spatial processes," Journal of Multivariate Analysis, Elsevier, vol. 112(C), pages 76-91.
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