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?

  • 3
    $\begingroup$ 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/ $\endgroup$ – Sal Mangiafico Jul 20 '17 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. $\endgroup$ – Michael R. Chernick Jul 20 '17 at 23:08
  • $\begingroup$ @MichaelChernick I meant that boot.ci will return. Clarified in the question. $\endgroup$ – dfrankow Jul 23 '17 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? $\endgroup$ – Michael R. Chernick Jul 23 '17 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. $\endgroup$ – Sal Mangiafico Jul 23 '17 at 22:47

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.

  • $\begingroup$ A cliched question: "If the number of replicates are small" -- how small is "small"? $\endgroup$ – Jabro Nov 13 '20 at 13:20

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