I have been reading around the literature and have been trying to work out the correct way (or most accurate way) to calculate a 68.3% confidence interval using bootstrapping for my particular data sample, but wasn't 100% clear so far.
I have a bootstrapped parameter distribution that is non-normal, and has a definite skew to the right (see attached image). It has been suggested to me to simply determine the confidence interval (which will be asymmetric around the mean in this case) by removing N * 0.5 * (1-0.683) of the N bootstrapping results from left and right and then taking these end points as the 15.85% and 84.15% quantiles. From reading around, it seems that for skewed and/or biased bootstrap parameter distributions (as is the case here) I should instead use the BCa bootstrap interval to determine the confidence intervals, as this will provide more accurate intervals with better coverage for this particular situation than the nominal method described above (which I think assumes normality of the parameter distribution?)
Is this the correct interpretation, and if so could someone please explain to me why?
Thanks in advance.