Bootstrap approaches for spatial data
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Generation of replicates of the available data enables the researchers to solve different statistical problems, such as the estimation of standard errors, the inference of parameters or even the approximation of distribution functions. With this aim, Bootstrap approaches are suggested in the current work, specifically designed for their application to spatial data, as they take into account the dependence structure of the underlying random process. The key idea is to construct nonparametric distribution estimators, adapted to the spatial setting, which are distribution functions themselves, associated to discrete or continuous random variables. Then, the Bootstrap samples are obtained by drawing at random from the estimated distribution. Consistency of the suggested approaches will be proved by assuming stationarity from the random process or by relaxing the latter hypothesis to admit a deterministic trend. Numerical studies for simulated data and a real data set, obtained from environmental monitoring, are included to illustrate the application of the proposed Bootstrap methods.
KeywordsDistribution estimation Resampling method Spatial data Stationarity Trend
Mathematics Subject Classification62G09 62M30
The authors would like to thank the helpful suggestions and comments from the Reviewers. The authors are also grateful to Dr. K. J. Duncan-Barlow (University of Vigo) for her contribution in the language revision. The first and third authors acknowledge financial support from the Project TEC2011-28683-C02-02 of the Spanish Ministry of Science and Innovation and the Project CN2012/279 from the European Regional Development Fund and the Galician Regional Government (Xunta de Galicia). The second author’s work has been supported by the Project PTDC/MAT/112338/2009 (FEDER support included) of the Portuguese Ministry of Science, Technology and Higher Education.