Abstract
A new method based on distances for modeling continuous random data in Gaussian random fields is presented. In non-stationary cases in which a trend or drift is present, dealing with information in regionalized mixed variables (including categorical, discrete and continuous variables) is common in geosciences and environmental sciences. The proposed distance-based method is used in a geostatistical model to estimate the trend and the covariance structure, which are key features in interpolation and monitoring problems. This strategy takes full advantage of the information at hand due to the relationship between observations, by using a spectral decomposition of a selected distance and the corresponding principal coordinates. Unconditional simulations are performed to validate the efficiency of the proposed method under a variety of scenarios, and the results show a statistical gain when compared with a more traditional detrending method. Finally, our method is illustrated with two applications: earth’s average daily temperatures in Croatia, and calcium concentration measured at a depth of 0–20 cm in Brazil.
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Notes
The intamap library of R was used (Pebesma et al. 2010), which gave an angle of − 70.11126 and a rate of 1.141188.
\(|N(h_j)|\) was considered for the weights.
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Acknowledgements
Work partially funded and supported by: Grant MTM2016-78917-R from the Spanish Ministry of Science and Education, Core Spatial Data Research (Faculty of Engineering, COL0013969, Universidad Distrital Francisco José de Caldas), and Applied Statistics in Experimental Research, Industry and Biotechnology (COL0004469, Universidad Nacional de Colombia). The authors are grateful to the AE and the referees for their helpful comments and suggestions that have improved the manuscript.
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Melo, C.E., Mateu, J. & Melo, O.O. A Distance-based Method for Spatial Prediction in the Presence of Trend. JABES 25, 315–338 (2020). https://doi.org/10.1007/s13253-020-00395-2
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DOI: https://doi.org/10.1007/s13253-020-00395-2