Quantile Estimation in Modified Ranked Set Sampling Methods

It is formally shown that ranked set sampling (RSS) and its variations produce estimators enjoying with many interesting properties. Although the problem of nonparametric quantile estimation has drawn much attention under RSS, it has not been addressed under RSS variations. To fill this gap, this article deals with the problem of estimating the population quantiles based on RSS and its variations which are pair RSS, and MiniMax RSS. Two quantiles estimators are proposed and their asymptotic distributions are also derived. Taking into account the information provided by the concomitant variable, additional three quantiles estimators are also introduced. The comprehensive simulation-based results reveal the superiority of all the proposed estimators, particularly the concomitant-based estimators, over their counterpart in simple random sampling among most of the considered cases as long as the ranking quality is fairly good. Finally, an empirical data set is also used to illustrate application of the proposed procedures.