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Bootstrap of the Mean in the Infinite Variance Case
Open accessAbstract
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.
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Cited by
Estimation and Inference in Nonparametric Frontier Models: Recent Developments and Perspectives
Simar, L., & Wilson, P. W. (2013) · Foundations and Trends in Econometrics · doi:10.1561/0800000020 · Cited by 382
A review of bootstrap confidence intervals
Diciccio, T. J., & Romano, J. P. (1988) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/j.2517-6161.1988.tb01732.x · Cited by 314
Metadata
- Authors
- Athreya, K. B.
- Venue
- The Annals of Statistics
- Publisher
- Institute of Mathematical Statistics
- Published
- 1987-06-01
- Volume
- 15
- Issue
- 2
- ISSN
- 0090-5364 (ISSN-L)
- OpenAlex
- W1976241708
- Cited by
- 230
- References
- 0
- FWCI
- 2.84
- Type
- journal article
- Language
- en
- Open access
- bronze
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- Athreya, K. B. (1987). Bootstrap of the Mean in the Infinite Variance Case. The Annals of Statistics. https://doi.org/10.1214/aos/1176350371
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
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