Copula-based multiple indicator kriging for non-Gaussian random fields

Embargo End Date
2023-06-09

Type
Article

Authors
Agarwal, Gaurav
Sun, Ying
Wang, Huixia J.

KAUST Department
Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division
Environmental Statistics Group
Statistics Program

KAUST Grant Number
OSR-2019-CRG7-3800

Online Publication Date
2021-06-09

Print Publication Date
2021-06

Date
2021-06-09

Submitted Date
2020-12-26

Abstract
In spatial statistics, the kriging predictor is the best linear predictor at unsampled locations, but not the optimal predictor for non-Gaussian processes. In this paper, we introduce a copula-based multiple indicator kriging model for the analysis of non-Gaussian spatial data by thresholding the spatial observations at a given set of quantile values. The proposed copula model allows for flexible marginal distributions while modeling the spatial dependence via copulas. We show that the covariances required by kriging have a direct link to the chosen copula function. We then develop a semiparametric estimation procedure. The proposed method provides the entire predictive distribution function at a new location, and thus allows for both point and interval predictions. The proposed method demonstrates better predictive performance than the commonly used variogram approach and Gaussian kriging in the simulation studies. We illustrate our methods on precipitation data in Spain during November 2019, and heavy metal dataset in topsoil along the river Meuse, and obtain probability exceedance maps.

Citation
Agarwal, G., Sun, Y., & Wang, H. J. (2021). Copula-based multiple indicator kriging for non-Gaussian random fields. Spatial Statistics, 100524. doi:10.1016/j.spasta.2021.100524

Acknowledgements
The research reported in this publication was supported by funding from King Abdullah University of Science and Technology (KAUST) under award number OSR-2019-CRG7-3800. The precipitation dataset used in this research was taken from the European Climate Assessment & Dataset (ECA&D) project available at https://www.ecad.eu.

Publisher
Elsevier BV

Journal
Spatial Statistics

DOI
10.1016/j.spasta.2021.100524

Additional Links
https://linkinghub.elsevier.com/retrieve/pii/S2211675321000348

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