Balanced modified systematic sampling in the presence of linear trend

Abstract

In the presence of linear trend, linear systematic sampling (LSS) is less efficient than stratified random sampling (STR) and more efficient than simple random sampling (SRS). Consequently, some authors have proposed modifications to the LSS design, which have shown to yield optimal results under certain conditions. In this paper, a further modified design, termed as balanced modified systematic sampling (BMSS), is proposed. BMSS is compared to various well-known modified LSS designs as well as LSS, SRS and STR. If half the sample size is an even integer, then BMSS is optimal. To obtain linear trend free sampling results for the other cases of the sample size, a BMSS with end corrections (BMSSEC) estimator is constructed. The results in this paper suggest that the proposed estimator performs better than all other estimators for odd sample sizes and even sampling intervals. Moreover, the proposed estimator is competitive for all other cases.