On The Theory Of Ranked-set Sampling And Its Application

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 considerde and it is proved that the method-of-moment estimates of parameters based on a GRSS sample will always have smaller asymptotic variance 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.