Athreya, K. B. Bootstrap of the mean in the infinite variance case. (English) Zbl 0628.62042 Ann. Stat. 15, 724-731 (1987). 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 Cited in 6 ReviewsCited in 70 Documents MSC: 62G05 Nonparametric estimation 62E20 Asymptotic distribution theory in statistics 60F05 Central limit and other weak theorems Keywords:infinite variance case; Poisson random measure; domain of attraction; stable law; bootstrap; normalized mean; random distribution; heavy tailed case × Cite Format Result Cite Review PDF Full Text: DOI