Confidence Interval from bootstrap To produce the , say, 95%, confidence interval(CI) from the bootstrap distribution, I know 2 approaches:
Approach 1: calculate the 2.5% and 97.5% percentile from the bootstrap distribution
Approach 2: bootstrap mean +/- 1.96*bootstrap SE
I would like to ask in which cases each approach will be more sensible and why so.
 A: Some ideas I have read about in Rand R. Wilcox - Fundamentals of Modern Statistical Methods, which by the way, it is a really nice book to read in general. 
Approach 1 which is called percentile bootstrap works well only if you have a pretty number of observations and it covers well the whole interval of interest. 
Approach 2 which is called percentile t bootstrap is slightly better for smaller samples than the previous samples. However it is interesting to check if the distribution resembles a normal distribution. If this is the case a t statistic is better than percentile t bootstrap. The bootstrap provides advantages only when the distribution is not normal.
I always used the second method. However what I do usually is to employ both methods and if they provides very different results than try to identify why that happened and chose the variant which makes those assumptions which fits better my data.
A: There are at least 4 or 5 types of Bootstrap confidence intervals (BCa, bootstrap-t, ABC, and calibration). These are thoroughly described here:
Bootstrap Confidence Intervals. Thomas J. DiCiccio and Bradley Efron
And they are all implemented in the 'boot' R package.
