Steady-state ranked set sampling for replicated environmental sampling designs

In replicated sampling protocols, each design replicate is independently and randomly placed onto the study region. Subsequently, in order to estimate the objective parameter, the Horvitz–Thompson (HT) estimator is usually considered for each design replicate and an overall estimator results from the average of the single estimators. Obviously, the procedure gives rise to a sample of HTestimators under simple random sampling (SRS) in such a way that the objective parameter is estimated by the corresponding sample mean. However, this procedure is likely to produce uneven coverage of the region and hence a large variability of the overall estimator. Therefore, to avoid such drawbacks, a quasi-systematic protocol for the design replicates is proposed. In this case, the suggested procedure gives rise to a sample of HT estimators under steady-state ranked set sampling (SRSS)–a generalization of well-known ranked set sampling (RSS)–so as to estimate the objective parameter by the corresponding sample mean. The proposed method produces large efficiency gains and does not involve supplementary sampling costs or extra field work.