Bootstrap approaches for spatial data

  • Pilar García-Soidán
  • Raquel Menezes
  • Óscar Rubiños
Article

Abstract

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.

Keywords

Distribution estimation Resampling method Spatial data Stationarity Trend 

Mathematics Subject Classification

62G09 62M30 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Pilar García-Soidán
    • 1
  • Raquel Menezes
    • 2
  • Óscar Rubiños
    • 3
  1. 1.Department of Statistics and Operations ResearchUniversity of VigoVigoSpain
  2. 2.Department of Mathematics and ApplicationsUniversity of MinhoBragaPortugal
  3. 3.Department of Signal Theory and CommunicationsUniversity of VigoVigoSpain

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