Remainder modified systematic sampling in the presence of linear trend

ABSTRACT

If the population size is not a multiple of the sample size, then the usual linear systematic sampling design is unattractive, since the sample size obtained will either vary, or be constant and different to the required sample size. Only a few modified systematic sampling designs are known to deal with this problem and in the presence of linear trend, most of these designs do not provide favorable results. In this paper, a modified systematic sampling design, known as remainder modified systematic sampling (RMSS), is introduced. There are seven cases of RMSS and the results in this paper suggest that the proposed design is favorable, regardless of each case, while providing linear trend-free sampling results for three of the seven cases. To obtain linear trend-free sampling for the other cases and thus improve results, an end corrections estimator is constructed.

KEYWORDS:

• Centered systematic sampling
• circular systematic sampling
• end corrections
• linear trend
• modified systematic sampling
• remainder linear systematic sampling.

MATHEMATICS SUBJECT CLASSIFICATION:

• 62D05

Acknowledgment

The authors would like to thank the NRF (National Research Foundation) for the funding that was provided during the production of this paper. Additionally, the authors are thankful to the referee for the valuable comments and suggestions that helped improve this paper.