I am reading the documentation of boot::abc.ci and feel I am missing something. It sounds like the "ABC" method is just an approximation of BCa bootstrap confidence intervals.
Is this the case? If so, when would we want to use that approximation instead of calculating the full BCa confidence interval? (The boot package calculates BCa intervals.)
Basically, there are situations where BCa intervals can become quite computationally expensive and ABC intervals offer a more feasible alternative. With the computational power usually at hands nowadays, I don't think there is so much need for ABC intervals anymore, though.
As reference, there is a brief statement about ABC methods in Puth et al. (2015):
[ABC methods] were developed as approximations to the BCa method that require much less computational effort. Increasing availability of computing power reduces concerns about computational effort [...] Further details of these methods can be found in Efron & Tibshirani (1993) or Manly (2007).
Puth, M. T., Neuhäuser, M., & Ruxton, G. D. (2015). On the variety of methods for calculating confidence intervals by bootstrapping. Journal of Animal Ecology, 84(4), 892-897. Link.
