Remainder linear systematic sampling with multiple random starts

Due to its simplicity and operational convenience, systematic sampling is one of the most prevalent sampling techniques. However, this sampling design has two main statistical drawbacks. First, the actual sample size is unfixed when the population size, N, is not an integral multiple of the desired sample size, n. Second, the sampling variance cannot be unbiasedly estimated on the basis of a single systematic sample. In this article we introduce a new generalized systematic sampling design that handles these two issues simultaneously. The proposed design combines the remainder linear systematic sampling design, which handles only the first problem, along with the idea of multistart systematic sampling that provides an unbiased estimator for the sampling variance. Unbiased estimators for both the finite population mean and the sampling variance are derived under the proposed design. The performance of the new design is evaluated relative to another six sampling schemes under several superpopulation models and real populations. Further, the stability of the proposed sampling variance estimator is studied. Applications of the suggested design are also discussed.