Model-Free Estimation from Spatial Samples: a Reappraisal of Classical Sampling Theory

A commonly held view among geostatisticians is that classical sampling theory is inapplicable to spatial sampling because spatial data are dependent, whereas classical sampling theory requires them to be independent. By comparing the assumptions and use of classical sampling theory with those of geostatistical theory, we conclude that this view is both false and unfortunate. In particular, estimates of spatial means based on classical sampling designs require fewer assumptions for their validity, and are therefore more robust, than those based on a geostatistical model.