Model-based variance estimation in non-measurable spatial designs

Two-dimensional systematic sampling and maximal stratification are frequently used in spatial surveys, because of their ease of implementation and design efficiency. An important drawback of these designs, however, is that no direct estimator of the design variance is available. In this paper estimation of the sampling variance of a total in a model- based context is considered. The estimation strategy is based on the use of the sample variogram which can be either a non-parametric or a parametric one. Consistency of the estimators is discussed; simulations and an application to real data show the good performance of the proposed procedure in practice.