Parameter estimation for concomitant and multivariate cluster ranked set sampling

The research presented in this thesis is concerned with ranked set sampling (RSS). Specifically we address an issue in ranked set sampling that goes largely ignored. Ranked set sampling assumes that items can be randomly selected from a population and then ranked on a variable of interest without actually taking measurements on the variable of interest. Visual ranking of tree heights is an oft cited example. However, if randomly selected items are not located in close proximity, the assumption that visual ranking can be performed may be violated. In this paper we investigate two methods for addressing this problem. First we consider ranking the observations on a concomitant variable. Second we examine the use of multivariate cluster sampling in the context of ranked set sampling. In each case we derive maximum likelihood estimates for the relevant parameters by framing ranked set sampling as a missing value problem. This leads to several interesting findings regarding simplification of density functions of multivariate order statistics.