## The Annals of Statistics

- Ann. Statist.
- Volume 17, Number 2 (1989), 684-691.

### Necessary Conditions for the Bootstrap of the Mean

#### Abstract

It is proved that $EX^2 < \infty$ is necessary for a very mild form of the bootstrap of the mean to work a.s. and that $X$ must be in the domain of attraction of the normal law if a.s. is weakened to "in probability."

#### Article information

**Source**

Ann. Statist. Volume 17, Number 2 (1989), 684-691.

**Dates**

First available: 12 April 2007

**Permanent link to this document**

http://projecteuclid.org/euclid.aos/1176347134

**JSTOR**

links.jstor.org

**Digital Object Identifier**

doi:10.1214/aos/1176347134

**Mathematical Reviews number (MathSciNet)**

MR994259

**Zentralblatt MATH identifier**

0672.62026

**Subjects**

Primary: 62E20: Asymptotic distribution theory

Secondary: 62F12: Asymptotic properties of estimators 60F05: Central limit and other weak theorems

**Keywords**

Bootstrap (of the mean) central limit theorem

#### Citation

Gine, Evarist; Zinn, Joel. Necessary Conditions for the Bootstrap of the Mean. The Annals of Statistics 17 (1989), no. 2, 684--691. doi:10.1214/aos/1176347134. http://projecteuclid.org/euclid.aos/1176347134.