## The Annals of Statistics

- Ann. Statist.
- Volume 17, Number 3 (1989), 1168-1175.

### On the Bootstrap of the Sample Mean in the Infinite Variance Case

#### Abstract

Athreya showed that the bootstrap distribution of a sum of infinite variance random variables did not (with probability 1) tend weakly to a fixed distribution but instead tended in distribution to a random distribution. In this paper, we give a different proof of Athreya's result motivated by a heuristic large sample representation of the bootstrap distribution.

#### Article information

**Source**

Ann. Statist., Volume 17, Number 3 (1989), 1168-1175.

**Dates**

First available in Project Euclid: 12 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aos/1176347262

**Digital Object Identifier**

doi:10.1214/aos/1176347262

**Mathematical Reviews number (MathSciNet)**

MR1015144

**Zentralblatt MATH identifier**

0687.62017

**JSTOR**

links.jstor.org

**Subjects**

Primary: 62E20: Asymptotic distribution theory

Secondary: 60B05: Probability measures on topological spaces 60G57: Random measures

**Keywords**

Bootstrap stable law random probability measures weak convergence

#### Citation

Knight, Keith. On the Bootstrap of the Sample Mean in the Infinite Variance Case. Ann. Statist. 17 (1989), no. 3, 1168--1175. doi:10.1214/aos/1176347262. https://projecteuclid.org/euclid.aos/1176347262