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When a parameter's sampling distribution is skewed, the bootstrap percentile confidence has coverage error (i.e. a 95% percent confidence interval is not really 95%).

See, for example, Bootstrap confidence intervals: when, which, what? A practical guide for medical statisticians by Carpenter and Bithell.

Is there any intuitive explanation why this is the case?

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  • $\begingroup$ The quick answer is that at its heart it relies on there being a reasonably good Normal approximation to the distribution of a monotonic transform of the statistic, and such a transform may not exist. Alternatively, you can think of it as representing the fact that, e.g., the $95^{th}$ bootstrap percentile of a sample of size $n$ from some distributions may be a seriously biased estimator of the $95^{th}$ percentile of the population (the bias decreases at $O(n^{-1/2})$ as $n \to \infty$.) $\endgroup$ – jbowman Feb 20 '18 at 17:31
  • $\begingroup$ Sample size of n refers to the number of observations and not the number of bootstrap repetitions, correct? $\endgroup$ – Great38 Feb 20 '18 at 17:47
  • $\begingroup$ Correct, increasing the number of bootstrap samples doesn't help with this particular problem. $\endgroup$ – jbowman Feb 20 '18 at 17:58

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