Exploiting nearest-neighbour maps for estimating the variance of sample mean in equal-probability systematic sampling of spatial populations

Abstract

Because of its ease of implementation, equal probability systematic sampling is of wide use in spatial surveys with sample mean that constitutes an unbiased estimator of population mean. A serious drawback, however, is that no unbiased estimator of the variance of the sample mean is available. As the search for an omnibus variance estimator able to provide reliable results under any spatial population has been lacking, we propose a design-consistent estimator that invariably converges to the true variance as the population and sample size increase. The proposal is based on the nearest-neighbour maps that are taken as pseudo-populations from which all the possible systematic samples can be enumerated. As nearest-neighbour maps are design-consistent under equal-probability systematic sampling and mild conditions, the variance of the sample mean achieved from all the possible systematic samples selected from the map is also a consistent estimator of the true variance. Through a simulation study based on artificial and real populations we show that our proposal generally outperforms the familiar estimators proposed in literature.