Mason and Newton  introduced the generalized (exchangeably weighted) bootstrap procedure and proved its consistency for the empirical distribution function, the quantile function and the mean. Surprisingly, Hájek's  results on the asymptotic behavior of the simple linear rank 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 powerful tool is Hájek's rank statistics methodology in the proof of a.s. consistency for various resampling schemes and to survey the existing results.
62G20, 62G10, 62G09