Bootstrap of the Mean in the Infinite Variance Case
Athreya, K. B.
Ann. Statist., Tome 15 (1987) no. 1, p. 724-731 / Harvested from Project Euclid
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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.
Publié le : 1987-06-14
Classification:  62E,  62F,  60F,  Bootstrap,  stable law,  Poisson random measure 
@article{1176350371,
     author = {Athreya, K. B.},
     title = {Bootstrap of the Mean in the Infinite Variance Case},
     journal = {Ann. Statist.},
     volume = {15},
     number = {1},
     year = {1987},
     pages = { 724-731},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176350371}
}

Athreya, K. B. Bootstrap of the Mean in the Infinite Variance Case. Ann. Statist., Tome 15 (1987) no. 1, pp.  724-731. http://gdmltest.u-ga.fr/item/1176350371/