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.
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.
MSC:
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 |