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March, 1985 Edgeworth Corrected Pivotal Statistics and the Bootstrap
Lavy Abramovitch, Kesar Singh
Ann. Statist. 13(1): 116-132 (March, 1985). DOI: 10.1214/aos/1176346580

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.

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Lavy Abramovitch. Kesar Singh. "Edgeworth Corrected Pivotal Statistics and the Bootstrap." Ann. Statist. 13 (1) 116 - 132, March, 1985. https://doi.org/10.1214/aos/1176346580

Information

Published: March, 1985
First available in Project Euclid: 12 April 2007

zbMATH: 0575.62018
MathSciNet: MR773156
Digital Object Identifier: 10.1214/aos/1176346580

Subjects:
Primary: 62E20
Secondary: 62G10, 62G15, 62G20

Rights: Copyright © 1985 Institute of Mathematical Statistics

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Vol.13 • No. 1 • March, 1985
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