Abstract
In geostatistics, the approximation of the spatial dependence structure of a process, through the estimation of the variogram or the covariogram of the variable under consideration, is an important issue. In this work, under a general spatial model, including a mean or trend function, and without assuming any parametric model for this function and for the dependence structure of the process, a general nonparametric estimator of the variogram is proposed. The new approach consists in applying an iterative algorithm, using the residuals obtained from a nonparametric local linear estimation of the trend function, jointly with a correction of the bias due to the use of these residuals. A simulation study checks the validity of the presented approaches in practice. The broad applicability of the procedures is demonstrated on a real data set.
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Acknowledgments
The authors thank two referees, and Jean Opsomer for very helpful comments and suggestions. The research of Rubén Fernández-Casal has been partially supported by MEC Grant MTM2008-03010. The research of Mario Francisco-Fernández has been partially supported by Grants MTM2008-00166 (ERDF included) and MTM2011-22392.
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Fernández-Casal, R., Francisco-Fernández, M. Nonparametric bias-corrected variogram estimation under non-constant trend. Stoch Environ Res Risk Assess 28, 1247–1259 (2014). https://doi.org/10.1007/s00477-013-0817-8
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DOI: https://doi.org/10.1007/s00477-013-0817-8