SPATIAL BREAKDOWN POINT OF VARIOGRAM ESTIMATORS

In the context of robust statistics, the breakdown point of an estimat or is an important feature of reliability. It measures the highest fra ction of contamination in the data that an estimator can support befor e being destroyed. In geostatistics, variogram estimators are based on measurements taken at various spatial locations. The classical notion of breakdown paint,leeds to be extended to a spatial one, depending o n the construction of most unfavorable configurations of perturbation. Explicit upper and lower bounds are available for the spatial breakdo wn point in the regular unidimensional case. The difficulties arising in the multidimensional case are presented on an easy example in R-2, as well as some simulations on irregular grids. In order to study the global effects of perturbations on variogram Estimators, further simul ations are carried out on data located on a regular or irregular bidim ensional grid. Results show that if variogram estimation is performed with a 50% classical breakdown point scale estimator, the number of in itial data likely to be contaminated before destruction of the estimat or is roughly 30% on average. Theoretical results confirm the previous statement on data in R-d, d greater than or equal to 1.