Statistica Sinica 11(2001), 23-37
Abstract: In this article, we consider the design of unbalanced ranked-set sampling in order to achieve certain optimality for inference on quantiles. We first derive the asymptotic properties of the unbalanced ranked-set sample quantiles for any unbalanced ranked-set sampling scheme. Then these properties are employed to develop a methodology for determining optimal ranked-set sampling schemes. In the case of inference on a single quantile, the optimal scheme results in an estimator of the quantile which is asymptotically unbiased and with minimum variance among all ranked-set sample (balanced or unbalanced) quantiles. The striking feature of the methodology is that it is distribution-free. The optimal schemes for inference on certain quantiles are computed. Some simulation studies are reported.
Key words and phrases: Asymptotic normality, Bahadur representation, optimal sampling design, quantile, ranked-set sampling.