Remainder Linear Systematic Sampling with Multiple Random Starts

Abstract

"Systematic sampling, either by itself or in combination with some other method, may be the most widely used method of sampling" (Levy (2008) p.83). This fact is due to the simplicity and the operational convenience of this technique. However, this technique has two main statistical problems. First, if the sampling interval, k=N/n, is not an integer, the actual sample size will not be fixed and the sample mean, y ̅, will not be unbiased estimator for Y ̅, the population mean. Second, regardless of the sampling interval, the sampling variance of the estimator y ̅ cannot be consistently estimated on the basis of a single systematic sample. In this study, we introduce a new generalized systematic sampling design that can handle these two issues simultaneously. The proposed design is a generalization of the remainder linear systematic sampling design of Chang and Huang (2000), which handles only the problem of non-integer sampling intervals. Unbiased estimators for both Y ̅ and the sampling variance are derived under the proposed design. The performance of the proposed design is evaluated in comparison to five sampling procedures under different supperpopulation models. Specifically, simple random sampling, remainder linear systematic sampling, circular systematic sampling, new partially systematic sampling and mixed random systematic sampling. It is found that our proposed design performs well compared to the other designs in most cases.