On ranked-set sample quantiles and their applications

Abstract

The properties of the sample quantiles of ranked-set samples are dealt with in this article. For any fixed set size in the ranked-set sampling the strong consistency and the asymptotic normality of the ranked-set sample quantiles for large samples are established. Bahadur representation of the ranked-set sample quantiles are also obtained. These properties are used to develop procedures for the inference on population quantiles such as confidence intervals and hypotheses testings. The efficiency of these procedures relative to their counterpart in simple random sampling is investigated. The ranked-set sampling is generally more efficient than the simple random sampling in this context. The gain in efficiency by using ranked-set sampling is quite substantial for the inference on middle quantiles and is the largest on the median. However, the relative efficiency damps away as the quantiles move away from the median on both directions. The gain in efficiency becomes negligible for extreme quantiles. © 2000 Elsevier Science B.V.