On some representations of the bootstrap (Q1111282)
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scientific article; zbMATH DE number 4076333
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On some representations of the bootstrap |
scientific article; zbMATH DE number 4076333 |
Statements
On some representations of the bootstrap (English)
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1989
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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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bootstrap statistic
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relatively negligible remainder
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quantiles
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convergence rates
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represenation
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uniform distribution
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