A variance estimator for systematic sampling from a deliberately ordered population

The systematic sampling (sys) design (Madow and Madow, 1944) is widely used by statistical offices due to its simplicity and efficiency (e.g., Iachan, 1982). But it suffers from a serious defect, namely, that it is impossible to unbiasedly estimate the sampling variance (Iachan, 1982) and usual variance estimators (Yates and Grundy, 1953) are inadequate and can overestimate the variance significantly (Sarndal et al., 1992). We propose a novel variance estimator which is less biased and that can be implemented with any given population order. We will justify this estimator theoretically and with a Monte Carlo simulation study.