A comparison of some robust estimators of the variogram for use in soil survey

The standard estimator of the variogram is sensitive to outlying data, a fe w of which can cause overestimation of the variogram. This will result in i ncorrect variances when estimating the value of a soil property by kriging or when designing a sampling grid to map the property to a required precisi on. Several robust estimators of the variogram, based on location and scale estimation, have been proposed as improvements. They seem to be suitable f or analysis of soil data in circumstances where the standard estimator is l ikely to be affected by outliers. Robust estimators are based on assumption s about the distribution of the data which will not always hold and which n eed not be made in kriging or in estimating the variogram by the standard e stimator. The estimators are reviewed. Simulation studies show that the robust estima tors vary in their susceptibility to moderate skew in the underlying distri bution, but that the effects of outliers are generally greater. The estimat ors are applied to some soil data, and the resulting variograms used for or dinary kriging at sites in a separate validation data set. In most cases th e variograms derived from the standard estimator gave kriging variances whi ch appeared to overestimate the mean squared error of prediction (MSEP). Kr iging with variograms based on robust estimators sometimes gave kriging var iances which underestimated the MSEP or did not differ significantly from i t. Estimates of kriging variance and the MSEP derived from the validation d ata were generally close to estimates from cross-validation on the predicti on set used to derive the variograms. This indicates that variogram models derived from different estimators could be compared by cross-validation.