Summary
The bootstrap statistic \(\hat \theta _n^* - \hat \theta _n \) is represented as the sum of two terms, one of which has the same distribution as \(\hat \theta _n - \theta \) and the other is a relatively negligible remainder. The representation is then applied to the problems of estimating a distribution and a quantile. The study includes the tail part of the distribution and quantiles for which the convergence rates could be faster than the usual “n -1/2” rate.
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Lo, SH. On some representations of the Bootstrap. Probab. Th. Rel. Fields 82, 411–418 (1989). https://doi.org/10.1007/BF00339995
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DOI: https://doi.org/10.1007/BF00339995
Keywords
- Stochastic Process
- Probability Theory
- Convergence Rate
- Statistical Theory
- Tail Part