Variance Estimation in Spatially Balanced Sampling

In spatially balanced sampling designs, joint inclusion probabilities for neighborhood units are often zero, or near to zero, because the sampling units tend to be spread across the sample space. In these cases it is difficult to use conventional estimators for the population variance. Alternative estimators, such as the neighborhood-based variance estimators have been introduced. The neighborhood-based variance estimator is recommended for use with Generalized Random Tessellation Stratified designs. In this paper, we review some of the currently available estimators, and introduce others, for use with spatially balanced sampling designs. In a simulation study, the efficiency of the introduced estimators are compared with different estimators under six spatially sampling designs (Balanced Acceptance Sampling, Halton Iterative Partitioning, Generalized Random Tessellation Stratified design, Spatially Correlated Poisson Sampling) and two local pivotal methods. In our simulation study the introduced estimators were more efficient than conventional ones.