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In wikipedia about disadvantage of bootstrap it says:

The apparent simplicity may conceal the fact that important assumptions are being made when undertaking the bootstrap analysis (e.g. independence of samples) where these would be more formally stated in other approaches.

Could you, please, explain this statement?

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    $\begingroup$ Related: Why does my bootstrap interval have terrible coverage? $\endgroup$
    – Stephan Kolassa
    Feb 20, 2020 at 10:09
  • $\begingroup$ I just do not understand the statement. $\endgroup$
    – ABK
    Feb 20, 2020 at 10:10
  • $\begingroup$ The samples of a bootstrap procedure are dependent but the obtained sampling distribution is treated as if it was created by iid values. $\endgroup$
    – 00schneider
    Feb 20, 2020 at 13:55

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  1. It's wiki, read all wiki with a grain of salt. You should raise a flag as being unclear, opinion-based, or needing a citation because all of those are (partly) true. The recent influx of people in statistics who feel that broad statements can be made and parroted without formal proof need to be reigned in (I include myself in that statement).

  2. The bootstrap does not require that samples are independent. There are special bootstrapping procedures that are more efficient than an unconditional bootstrap

  3. The article makes the critical fallacy of conflating the procedure of generating bootstrap replicates of a dataset (which has no assumptions whatsoever) and obtaining bootstrap intervals/p-values for a test statistic. The BCa, Quantile, Normal Percentile, and Double Bootstrap methods are just a subset of what's out there, and are all developed to be performed on already-bootstrapped replicates of the study data. Basically, there is no one method for getting CIs and p-values, and the weirdness ends up being more a function of the statistic chosen than it is an attribute of the data themselves.

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  • $\begingroup$ The bootstrap does not require that samples are independent. I think this should be expanded on for a more useful answer. For example, the cluster bootstrap doesn't require individual observations to be independent, but it does require clusters to be! Block bootstrap for time series is a more interesting case, but I'm not sure how that's asymptotically justified (not saying it's not, just saying it's beyond me). At the very least, the "vanilla" bootstrap most people think of does require independence. $\endgroup$
    – Cliff AB
    Feb 20, 2020 at 19:12
  • $\begingroup$ @CliffAB I would argue those are considerations for efficiency, but not necessarily for inference. If you use unconditional bootstrap in a sample with correlation, and estimate the GLS parameters in each subsample, the estimates become more widely varied due to the added variability in cluster size, but no other impact. Blocked bootstrap would improve efficiency. $\endgroup$
    – AdamO
    Feb 20, 2020 at 19:24
  • $\begingroup$ I'm afraid I don't understand your comment: if you ignored the correlations within clusters and sampled individual units instead of blocks, your bootstrap estimate of the standard error (for example) would have a huge bias and not be a consistent estimator. Thus inference would be invalid. $\endgroup$
    – Cliff AB
    Feb 20, 2020 at 20:46
  • $\begingroup$ @CliffAB using a weighted bootstrap to estimate between- or within- cluster variance has certainly the same attractive traits as performing a weighted sample. But I would say in your case that you are using the wrong variance estimator. The GLS variance estimator should be used in the bootstrapped sample. $\endgroup$
    – AdamO
    Feb 20, 2020 at 22:38
  • $\begingroup$ Now I'm more confused: why would you use the GLS variance estimator rather than using the bootstrap estimate of the standard errors? For reference, I'm referring to using a cluster bootstrap to address correlated samples, i.e., en.wikipedia.org/wiki/… $\endgroup$
    – Cliff AB
    Feb 20, 2020 at 23:11
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This may be related to the fact that the bootstrap may sometimes be roughly presented as an "assumption free" procedure that can be used to replace other common e.g. tests when their required assumptions (e.g. normality) are not met. However, bootstrapping is relevant only in certain situations raising assumptions that also have to be met.

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