## The Annals of Statistics

### Theoretical Comparison of Bootstrap Confidence Intervals

Peter Hall

#### Abstract

We develop a unified framework within which many commonly used bootstrap critical points and confidence intervals may be discussed and compared. In all, seven different bootstrap methods are examined, each being usable in both parametric and nonparametric contexts. Emphasis is on the way in which the methods cope with first- and second-order departures from normality. Percentile-$t$ and accelerated bias-correction emerge as the most promising of existing techniques. Certain other methods are shown to lead to serious errors in coverage and position of critical point. An alternative approach, based on "shortest" bootstrap confidence intervals, is developed. We also make several more technical contributions. In particular, we confirm Efron's conjecture that accelerated bias-correction is second-order correct in a variety of multivariate circumstances, and give a simple interpretation of the acceleration constant.

#### Article information

Source
Ann. Statist. Volume 16, Number 3 (1988), 927-953.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176350933

Digital Object Identifier
doi:10.1214/aos/1176350933

Mathematical Reviews number (MathSciNet)
MR959185

Zentralblatt MATH identifier
0663.62046

JSTOR