On the Bootstrap of the Sample Mean in the Infinite Variance Case
The Annals of Statistics · 1989 · Volume 17 · Issue 3
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.
Keywords
60B05, 60G57, 62E20, bootstrap, random probability measures, Stable law, weak convergence
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