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In the R 'boot' package, there is the option to output confidence intervals for bootstrapped estimates to be reported alongside the estimate itself, the estimated bias and the estimated standard error. CIs in the boot package are: normal, basic, percentile and bias-corrected/accelerated.

Is there any particular setting(s) where one CI type should be favoured over another? For instance, the bootstrap percentile CI is likely a very crude interval, whereas the BCa interval, while highly favoured, can produce unstable results.

My intuition is that one should report all 4 intervals, and indeed many applied statistics papers adhere to this.

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I think it helps to look at the various confidence intervals and see how similar they are. If they are close to the same it doesn't make much difference and the simpler methods might be preferred. The shape of the distribution that generates the original sample can make a difference. As an example Schenker (1985) using data from a chi square distribution with 19 degrees of freedom showed that the BC method didn't work very well and BCa was actually devised to overcome the problem. A good discussion of this can be found in the first or second edition of my book (Chernick 1999 and 2007)as well as in the Efron and Tibshirani (1986) text.

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  • $\begingroup$ Thank you Michael! I will definitely look into your book. My estimates from the bootstrap tend to be left-skewed, but this diminishes with larger sample size as expected. The bootstrap CIs are all very similar to one another, so perhaps I will report them all, or see which ones are most appropriate for my application area. $\endgroup$ – compbiostats Sep 8 '17 at 23:29

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