RANK STATISTICS APPROACH IN GENERALIZED BOOTSTRAP

Mason and Newton [8] introduced the generalized (exchangeably weighted ) bootstrap procedure and proved its consistency for the empirical dis tribution function, the quantile function and the mean. Surprisingly, Hajek's [2] results on the asymptotic behavior of the simple linear ra nk statistics play the crucial role in the proof. Mason-Newton's work inspired several authors who applied this method successfully to other types of statistics. The purpose of the paper is to point out how pow erful tool is Hajek's rank statistics methodology in the proof of a.s. consistency for various resampling schemes and to survey the existing results.