On the bootstrap of the sample mean in the infinite variance case. (English) Zbl 0687.62017

Knight, Keith

Ann. Stat. 17, No. 3, 1168-1175 (1989).

Summary: K. B. Athreya [ibid. 15, 724-731 (1987; Zbl 0628.62042)] 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 representaion of the bootstrap distribution.

MSC:

62E20	Asymptotic distribution theory in statistics
60B05	Probability measures on topological spaces
60F05	Central limit and other weak theorems
60G57	Random measures

Keywords:

stable law; weak convergence; bootstrap distribution of a sum of infinite variance random; variables; random distribution; large sample representaion of the bootstrap distribution; bootstrap distribution of a sum of infinite variance random variables

Citations:

Zbl 0628.62042