Design based estimation for ranked set sampling in finite populations

In this paper, we consider design-based estimation using ranked set sampling (RSS) in finite populations. We first derive the first and second-order inclusion probabilities for an RSS design and present two Horvitz–Thompson type estimators using these inclusion probabilities. We also develop an alternate Hansen–Hurwitz type estimator and investigate its properties. In particular, we show that this alternate estimator always outperforms the usual Hansen–Hurwitz type estimator in the simple random sampling with replacement design with comparable sample size. We also develop formulae for ratio estimator for all three developed estimators. The theoretical results are augmented by numerical and simulation studies as well as a case study using a well known data set. These show that RSS design can yield a substantial improvement in efficiency over the usual simple random sampling design in finite populations.