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I know that the regular bootstrap (assuming that the necessary assumptions are valid) is more efficient than the m-n bootstrap. However, supposing that you have access to really large data (such as a 1% sample of Google's daily searches), does it ever make sense to use the regular bootstrap whose assumptions may be violated? |
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As the author of texts on the bootstrap, I think I can provide a meaningful answer. There are very few assumptions to violate with the regular bootstrap. The issue with the bootstrap is whether or not it provides consistent estimates for the particular problem. When the ordinary (i.e., the usual $n$-out-of-$n$) bootstrap is consistent, $m$-out-of-$n$ is less efficient and there is no reason to use it over the ordinary bootstrap. The $m$-out-of-$n$ bootstrap comes in handy for the few exceptional cases where the ordinary bootstrap fails. In cases such as estimating extremes the ordinary bootstrap fails, but $m$-out-of-$n$ has been shown to be consistent as long as m goes to infinity at a slower rate than $n$. Then $m$-out-of-$n$ should be used. A practical question might be what to take for $m$. I would suggest something simple like square root of $n$. |
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