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Edgeworth corrected pivotal statistics and the bootstrap. (English) Zbl 0575.62018
A general procedure for multistage modification of pivotal statistics is developed to improve the normal approximation. Bootstrapping a first stage modified statistic is shown to be equivalent, in terms of asymptotic order, to the normal approximation of a second stage modification.
Explicit formulae are given for some basic cases involving independent random samples and samples drawn without replacement. The Hodges-Lehmann deficiency is calculated to compare the regular t-statistic with its one- step correction.

62E20 Asymptotic distribution theory in statistics
62D05 Sampling theory, sample surveys
62G10 Nonparametric hypothesis testing
62G15 Nonparametric tolerance and confidence regions
62G20 Asymptotic properties of nonparametric inference
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