Variance approximation under balanced sampling plans excluding adjacent units

Hedayat, Rao and Stufken (1988a, 1988b) first introduced balanced sampling plans for the exclusion of contiguous units. Sampling plans that exclude the selection of contiguous units within a given sample, while maintaining a constant second-order inclusion probability for non-contiguous units, were investigated for finite populations of N units arranged in a circular, one-dimensional ordering. Although significant advancements have been achieved concerning the generalization and existence of such sampling plans for finite, one-dimensional populations, many other aspects of these plans warrant further investigation. We present the results of an investigation of three biased estimators of the variance of the Horvitz Thompson estimator of the population mean under such plans.