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A rank statistics approach to the consistency of a general bootstrap. (English) Zbl 0777.62045

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.

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

Citations:

Zbl 0406.62024
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