Mason, David M.; Newton, Michael A. A rank statistics approach to the consistency of a general bootstrap. (English) Zbl 0777.62045 Ann. Stat. 20, No. 3, 1611-1624 (1992). Summary: 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 B. Efron [ibid. 7, 1-26 (1979; Zbl 0406.62024)] and D. Rubin [ibid. 9, 130-134 (1981)] among others, is proved by classical linear rank statistics theory. The consistency of generalized bootstrapped empirical and quantile processes is also established. Cited in 7 ReviewsCited in 77 Documents MSC: 62G09 Nonparametric statistical resampling methods 60F05 Central limit and other weak theorems 62G20 Asymptotic properties of nonparametric inference 62G30 Order statistics; empirical distribution functions Keywords:empirical processes; central limit theorem; exchangeably weighting sample points; generalized bootstrapped mean; linear rank statistics; consistency; quantile processes Citations:Zbl 0406.62024 PDFBibTeX XMLCite \textit{D. M. Mason} and \textit{M. A. Newton}, Ann. Stat. 20, No. 3, 1611--1624 (1992; Zbl 0777.62045) Full Text: DOI