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The boot.ci documentation in R says there are five different types of confidence interval that boot.ci will return:

  • norm (normal approximation)
  • basic
  • stud (studentized)
  • perc (percentile)
  • bca (bias-corrected, accelerated)

BCa looked pretty good, but it seems really slow for my data.

How should I choose which one to use?

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    $\begingroup$ From what I've read, BCa and percentile are considered the technically superior. I have found percentile to be reasonably well behaved in difficult situations (e.g. small sample size or discontinuous data). The following article is helpful: tau.ac.il/~saharon/Boot/10.1.1.133.8405.pdf $\endgroup$ Commented Jul 20, 2017 at 22:49
  • $\begingroup$ There are actually more than 5. There is BC which does not include the use of an acceleration constant, two percentile methods (Efron's and Hall's) and iterated bootstrap. $\endgroup$ Commented Jul 20, 2017 at 23:08
  • $\begingroup$ @MichaelChernick I meant that boot.ci will return. Clarified in the question. $\endgroup$
    – dfrankow
    Commented Jul 23, 2017 at 14:37
  • $\begingroup$ So the procedure will give you only those 5 choices. But percentile method is ambiguous. Is it Efron's or Hall's percentile method? $\endgroup$ Commented Jul 23, 2017 at 15:16
  • $\begingroup$ The documentation for boot.ci says, "The formulae on which the calculations are based can be found in Chapter 5 of Davison and Hinkley (1997)." Dunno if that's helpful. $\endgroup$ Commented Jul 23, 2017 at 22:47

2 Answers 2

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If your replicates are not normally distributed, do not choose $normal$.

$Basic$ can give you intervals that are out of the range of your replicated data; e.g. your bootstrapped replicates range between 2-200 but your lower confidence interval is -5.

For $student's$ CI, you need to pass a variance alongside whatever statistics (e.g. mean, median) you are dealing with. I would prefer this over $bca$ if you cannot generate a large number of replicates that can satisfy $bca$. If the number of replicates are small, the $bca$ intervals become unstable. One way of checking the stability is to generate many sets of replicates and identify corresponding confidence limits - most likely you will notice that the range of confidence limits based on $bca$ is wider than the rest.

I don't even know why they have the $percentile$ method, the most confusing of all five.

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    $\begingroup$ A cliched question: "If the number of replicates are small" -- how small is "small"? $\endgroup$
    – Rafs
    Commented Nov 13, 2020 at 13:20
  • $\begingroup$ I appreciate your answer. Ironically, while you find percentile the most confusing, I see it recommended in a lot of places, because it's conceptually simple (just take 2.5 and 97.5 percentile). I don't know whether it's good. I thought I read in a paper by Efron et al. that it can be biased, hence the BCa. $\endgroup$
    – dfrankow
    Commented Aug 15, 2022 at 18:07
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I found https://arxiv.org/abs/1411.5279 to be one of the clearest and easiest-to-read reference.

In contrast to other sources the author recommends to avoid the basic confidence interval and rather use the easy percentile or some t-test based one. I'm not sure whether it touches upon BCA.

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