An application of the deterministic variogram to design-based variance estimation

When estimating the mean value of a variable, or the total amount of a resource, within a specified region it is desirable to report an estimated standard error for the resulting estimate. If the sample sites are selected according to a probability sampling design, it usually is possible to construct an appropriate design-based standard error estimate. One exception is systematic sampling for which no such standard error estimator exists. However, a slight modification of systematic sampling, termed 2-step tessellation stratified (2TS) sampling, does permit the estimation of design-based standard errors. This paper develops a design-based standard error estimator for 2TS sampling. It is shown that the Taylor series approximation to the variance of the sample mean under 2TS sampling may be expressed in terms of either a deterministic variogram or a deterministic covariance function. Variance estimation then can be approached through the estimation of a variogram or a covariance function. The resulting standard error estimators are compared to some more traditional variance estimators through a simulation study. The simulation results show that estimators based on the new approach may perform better than traditional variance estimators.