Robust Semivariogram Estimation in the Presence of Influential Spatial Data Values

Abstract

Semivariogram modeling is central to the prediction of point values and areal averages of geostatistical random fields. Additionally, estimates of semivariogram model parameters themselves are of intrinsic interest because of the information they provide about spatial dependence across a region. The fitting of semivariogram models is in turn critically dependent on the shape of sample semivariogram plots. Basu et al. (1995) document that the presence of influential spatial data values can seriously distort sample semivariogram plots and can affect both the choice of semivariogram models and the estimation of model parameters. Moreover, they found that the application of some of the more popular robust methods to data files containing influential data does not always satisfactorily accommodate these influential observations. In this paper, we discuss several robust estimators of semivariogram values that aid in the identification and accommodation of influential spatial data values and that can be used with very large data sets where it is sometimes prohibitive to interactively investigate the presence of influential observations.