This paper proposes robust estimators of the variogram, a statistical tool that is commonly used in geostatistics to capture the spatial dependence structure of data. The new estimators are based on the highly robust minimum covariance determinant estimator and estimate the directional variogram for several lags jointly. Simulations and breakdown considerations confirm the good robustness properties of the new estimators. While Genton's estimator based on the robust estimation of the variance of pairwise sums and differences performs well in case of isolated outliers, the new estimators based on robust estimation of multivariate variance and covariance matrices perform superior to the established alternatives in the presence of outlier blocks in the data. The methods are illustrated by an application to satellite data, where outlier blocks may occur because of e.g. clouds.

翻译：本文提出了变异函数的稳健估计方法，变异函数是地统计学中用于捕捉数据空间依赖结构的常用统计工具。新估计器基于高度稳健的最小协方差行列式估计量，可联合估计多个滞后距的方向变异函数。模拟实验与崩溃点分析证实了新估计器良好的稳健性。虽然基于成对和与差方差稳健估计的Genton估计器在孤立异常值情况下表现良好，但基于多元方差与协方差矩阵稳健估计的新估计器在数据存在异常块时，其性能优于现有替代方法。本文通过卫星数据应用实例说明了这些方法，其中异常块可能由云层等因素导致。