On ranked-set sample quantiles and their applications (original) (raw)

The properties of the sample quantiles of ranked-set samples are dealt with in this article. For any ÿxed 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 conÿdence intervals and hypotheses testings. The e ciency of these procedures relative to their counterpart in simple random sampling is investigated. The ranked-set sampling is generally more e cient than the simple random sampling in this context. The gain in e ciency by using ranked-set sampling is quite substantial for the inference on middle quantiles and is the largest on the median. However, the relative e ciency damps away as the quantiles move away from the median on both directions. The gain in e ciency becomes negligible for extreme quantiles.