## The Annals of Statistics

### Edgeworth Corrected Pivotal Statistics and the Bootstrap

#### 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.

#### Article information

Source
Ann. Statist., Volume 13, Number 1 (1985), 116-132.

Dates
First available in Project Euclid: 12 April 2007

https://projecteuclid.org/euclid.aos/1176346580

Digital Object Identifier
doi:10.1214/aos/1176346580

Mathematical Reviews number (MathSciNet)
MR773156

Zentralblatt MATH identifier
0575.62018

JSTOR

#### Citation

Abramovitch, Lavy; Singh, Kesar. Edgeworth Corrected Pivotal Statistics and the Bootstrap. Ann. Statist. 13 (1985), no. 1, 116--132. doi:10.1214/aos/1176346580. https://projecteuclid.org/euclid.aos/1176346580