Fixed-domain asymptotics for variograms using subsampling

The variogram is a measure of the local variation in space of a random fiel d. For large geostatistical data sets, the traditional empirical variogram may be hard to compute. This article presents, for processes with a fixed d omain, the effect of using a subsample of the available data on the perform ance of the empirical variogram. The motivation of this work, apart from th e saving on computation, is to study how dense the observations need to be in the bounded sampling region to obtain most of the information we would g el from continuous observations in the fixed domain.