On the Bootstrap of the Sample Mean in the Infinite Variance Case
Keith Knight · The Annals of Statistics · 1989
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.