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Bootstrap of the mean in the infinite variance case. (English) Zbl 0628.62042
Author’s summary: Let \(X_ 1,X_ 2,...,X_ n\) 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.
Reviewer: Zhao Lincheng

62G05 Nonparametric estimation
62E20 Asymptotic distribution theory in statistics
60F05 Central limit and other weak theorems
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