Model-based variance estimation in non-measurable spatial designs

- The proposed estimation strategy takes into account the structure of spatial dependence through the use of the variogram.
- Properties of the estimators are discussed.
- Application of the important case of stratified spatial sampling with one unit per stratum and two-dimensional systematic sampling are presented.

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.