Estimating the variance of the sample mean in two-dimensional systematic sampling

This article investigates the problem of estimating the sampling error when the population mean (total) is estimated from a single two-dimensional systematic sample. In particular, two-dimensional extensions of known approximate variance estimators used in linear systematic sampling are introduced. These almost new variance estimators have the advantage of taking into account the spatial ordering of sample units and, consequently, the spatial autocorrelation among them. An investigation of their properties is carried out through a series of simulations and an empirical study.