Asymptotic theory for bootstrapping the extremes
- 1 January 1992
- journal article
- research article
- Published by Taylor & Francis in Communications in Statistics - Theory and Methods
- Vol. 22 (1) , 15-30
- https://doi.org/10.1080/03610929308831003
Abstract
This paper considers asymptotic analysis of bootstrap distributions for the extremes from an iid sample. In contrast to the case of almost sure convergence to a fixed (normal) distribution in the case of the sample mean (finite variance case), the bootstrap distribution of an extreme tends in distribution to a random probability measure. These results are similar to the result for the bootstrap distribution of the sample mean in the infinite variance case where the underlying random variables are in the domain of attraction of a stable law with index αε(0,2).Keywords
This publication has 8 references indexed in Scilit:
- On the Bootstrap of the Sample Mean in the Infinite Variance CaseThe Annals of Statistics, 1989
- A note on the central limit theorem for the bootstrap meanCommunications in Statistics - Theory and Methods, 1989
- A Central Limit Theorem for the Bootstrap MeanThe American Statistician, 1988
- Bootstrap of the Mean in the Infinite Variance CaseThe Annals of Statistics, 1987
- Some Asymptotic Theory for the BootstrapThe Annals of Statistics, 1981
- Convergence to a Stable Distribution Via Order StatisticsThe Annals of Probability, 1981
- Approximation Theorems of Mathematical StatisticsPublished by Wiley ,1980
- Probability TheoryPublished by Springer Nature ,1978