Confidence intervals for quantiles in finite populations with randomized nomination sampling

Given a finite population consisting of NN elements, it is desired to obtain confidence intervals for (t/N)(t/N)th quantile x(t)x(t) of the population based on the randomized nomination sampling (RNS) design. Three without replacement sampling protocols are described and procedures for constructing nonparametric confidence intervals for population quantiles are developed. Formulas for computing coverage probabilities for these confidence intervals are presented. Simulation studies are conducted and the performance of the RNS based confidence intervals is compared with those based on the simple random sample without replacement design.