Translator Disclaimer
June, 1987 Bootstrap of the Mean in the Infinite Variance Case
K. B. Athreya
Ann. Statist. 15(2): 724-731 (June, 1987). DOI: 10.1214/aos/1176350371

Abstract

Let $X_1, X_2, \ldots, X_n$ be independent identically distributed random variables with $EX^2_1 = \infty$ but $X_1$ belonging to the domain of attraction of a stable law. It is known that the sample mean $\bar{X}_n$ appropriately normalized converges to a stable law. It is shown here that the bootstrap version of the normalized mean has a random distribution (given the sample) whose limit is also a random distribution implying that the naive bootstrap could fail in the heavy tailed case.

Citation

Download Citation

K. B. Athreya. "Bootstrap of the Mean in the Infinite Variance Case." Ann. Statist. 15 (2) 724 - 731, June, 1987. https://doi.org/10.1214/aos/1176350371

Information

Published: June, 1987
First available in Project Euclid: 12 April 2007

zbMATH: 0628.62042
MathSciNet: MR888436
Digital Object Identifier: 10.1214/aos/1176350371

Rights: Copyright © 1987 Institute of Mathematical Statistics

JOURNAL ARTICLE
8 PAGES


SHARE
Vol.15 • No. 2 • June, 1987
Back to Top