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On bootstrap iteration for coverage correction in confidence intervals. (English) Zbl 0736.62040
The author focuses on the use of the iterated resampling principle introduced by him and {\it P. Hall} [Biometrika 75, 661-671 (1988; Zbl 0659.62053)] to reduce coverage error in confidence intervals. He proves that in the case of one-sided confidence intervals each iteration of the coverage-correction algorithm reduces coverage error by a factor of order $n\sp{-1/2}$, whereas for two-sided intervals the reduction in error is by a factor of order $n\sp{-1}$. He also provides explicit formulas for dominant remainder terms in expansions of coverage error after bootstrap iteration in both one- and two-sided cases. Some illustrative applications are given.

62G15Nonparametric tolerance and confidence regions
62G09Nonparametric statistical resampling methods
62F25Parametric tolerance and confidence regions
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