Statistics and Computing

, Volume 21, Issue 1, pp 107–120 | Cite as

Estimating and testing zones of abrupt change for spatial data

  • Edith Gabriel
  • Denis Allard
  • Jean-Noël Bacro


We propose a method for detecting the zones where a variable irregularly sampled in the plane changes abruptly. Our general model is that under the null hypothesis the variable is the realisation of a stationary Gaussian process with constant expectation. The alternative is that the mean function presents abrupt changes. We define potential Zones of Abrupt Change (ZACs) by the points where the gradient, estimated under the null hypothesis, exceeds a determined threshold. We then design a global test to assess the global significance of the potential ZACs, an issue missing in all existing methods. The theory that links the threshold and the global level is based on asymptotic distributions of excursion sets of non-stationary χ 2 fields for which we provide new results. The method is evaluated by a simulation study and applied to a soil data set in the context of precision agriculture.


Excursion set Gaussian random fields Geostatistics Gradient estimation χ2 random fields Wombling 


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© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.Unité de Biostatistique et Processus SpatiauxInstitut National de la Recherche AgronomiqueAvignonFrance
  2. 2.I3M, UMR CNRS 5149Université Montpellier IIMontpellierFrance

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