A general notion of a bootstrapped mean constructed by exchangeably weighting sample points is introduced. Consistency of this generalized bootstrapped mean, which includes proposals of Efron and Rubin among others, is proved by classical linear rank statistics theory. The consistency of generalized bootstrapped empirical and quantile processes is also established.
"A Rank Statistics Approach to the Consistency of a General Bootstrap." Ann. Statist. 20 (3) 1611 - 1624, September, 1992. https://doi.org/10.1214/aos/1176348787