The Annals of Statistics

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

Keith Knight

Full-text: Open access

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


Export citation