On the theory of ranked-set sampling and its ramifications

Abstract

We consider in this article ranked-set sampling (RSS) and its ramifications including RSS with imperfect ranking, RSS by ranking a concomitant variable and RSS with multivariate samples, etc. We deal with a unified sampling scheme which is referred to as generalized ranked-set sampling (GRSS) and which includes RSS and its ramifications as special cases. We develop a general theory for GRSS in both parametric and nonparametric settings. In a parametric setting, it is shown that the Fisher information matrix about the unknown parameters of a GRSS sample minus that of an SRS sample of the same size is always positive definite. In a nonparametric setting, a particular model, the smooth-function-of-means model, is considered and it is proved that the method-of-moment estimates of parameters based on a GRSS sample will always have smaller asymptotic variances than those based on an SRS sample of the same size. An example for RSS with multivariate samples is treated in detail and a simulation study is reported. Some other issues and open problems such as those involving optimal designs for the GRSS are also discussed. © 2002 Elsevier Science B.V. All rights reserved.