Nonparametric directional variogram estimation in the presence of outlier blocks

TL;DR

This paper introduces robust, nonparametric estimators for directional variograms in geostatistics that effectively handle outlier blocks, outperforming existing methods especially in contaminated data scenarios.

Contribution

It develops new robust estimators based on the minimum covariance determinant that jointly estimate directional variograms and demonstrate superior robustness against outlier blocks.

Findings

New estimators show high robustness in simulations.

Outperform existing methods in presence of outlier blocks.

Effective in real satellite data with cloud-induced outliers.

Abstract

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.