Edgeworth Corrected Pivotal Statistics and the Bootstrap
The Annals of Statistics · 1985 · Volume 13 · Issue 1
Abstract
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.
Keywords
62E20, 62G10, 62G15, 62G20, bootstrap procedure, confidence intervals, Edgeworth expansions, Hypothesis testing, Pivotal statistics, random sampling without replacement
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