Spatial breakdown point of variogram estimators

Marc G. Genton*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

23 Scopus citations


In the context of robust statistics, the breakdown point of an estimator is an important feature of reliability. It measures the highest fraction of contamination in the data that an estimator can support before being destroyed. In geostatistics, variogram estimators are based on measurements taken at various spatial locations. The classical notion of breakdown point needs to be extended to a spatial one, depending on the construction of most unfavorable configurations of perturbation. Explicit upper and lower bounds are available for the spatial breakdown point in the regular unidimensional case. The difficulties arising in the multidimensional case are presented on an easy example in IR2, as well as some simulations on irregular grids. In order to study the global effects of perturbations on variogram estimators, further simulations are carried out on data located on a regular or irregular bidimensional grid. Results show that if variogram estimation is performed with a 50% classical breakdown point scale estimator, the number of initial data likely to be contaminated before destruction of the estimator is roughly 30% on average. Theoretical results confirm the previous statement on data in IR(d), d ≥ 1.

Original languageEnglish (US)
Pages (from-to)853-871
Number of pages19
JournalMathematical Geology
Issue number7
StatePublished - 1998
Externally publishedYes


  • Classical breakdown point
  • Robustness
  • Scale estimation
  • Spatial statistics

ASJC Scopus subject areas

  • Mathematics (miscellaneous)
  • Earth and Planetary Sciences (miscellaneous)


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