This bootstrap primer from Stanford says

How many observations should we resample? A good suggestion is the original sample size.

While I get that this advice might be referring specifically to the study example in that guide, is it "a good suggestion" in general? Under what circumstances might be more appropriate to resample smaller or larger than the original sample size?

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    $\begingroup$ Look at the m out of n bootstrap. It uses a sample size m less than n but always increasing as n increases. It tends to infinity as n odes. There is no case tht I am familar with where m is chosen greater than n. $\endgroup$ – Michael Chernick Jan 25 '17 at 4:01
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    $\begingroup$ It is opinion based, but I believe that a bootstrap sample smaller than the original dataset will not be representative of the variability and might be too imprecise. Conversely, a much larger one will be too precise and thus also not representative of the original sample. The choice might also have historical reasons, with bootstrap evolving from jacknife, whose sample cannot ever be larger than the original one. $\endgroup$ – Joe_74 Jan 25 '17 at 5:54
  • $\begingroup$ @Joe_74 Do you think that your comment remains true if we are using the bootstrap for the purposes of model comparison/selection, rather than applying it to estimate CIs/precision? $\endgroup$ – user1205901 Jan 25 '17 at 6:09
  • $\begingroup$ @user1205901 I guess so, as even for model building and external validation Ewout Steyerberg typically recommends same size samples. $\endgroup$ – Joe_74 Jan 25 '17 at 8:07

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