I have reviewed a number of questions, but so far there is no clear answer on exactly which algorithms/procedures are implemented in boot.ci for R. For instance, 292619 mentions the types of intervals given but there it is in the context of selecting one of them, not defining the method.
The intervals are listed as:
- Normal
- Basic
- Studentized (Likely the bootstrap t, as in this paper, p. 1150)
- Percentile
- BCa (This one "appears" clearly defined!)
Unfortunately, these terms are not unambiguous as Michael Chernick points out, it is not clear if the percentile method is Efron's or Hall's (see comments on question). Additionally there is no clear linking from these methods to the sources. Nor do the docs is R clarify these points.
For instance, is the "normal" in this function the normal interval estimated by using the variance of the bootstrap distribution in the construction of the usual normal-theory CI? Or is that one the "basic" bootstrap? See here, page 216, if you can access this.
Is there a definitive source that lists the methods implemented and where the algorithms come from? Preferably a source that is available without trying to get a textbook?
Best Answer
From their help and code they have:
Normal: Using the normal approximation to a statistic, calculate equi-tailed two-sided confidence intervals.
Basic: Normal approximation method for confidence intervals. This can be used with or without a bootstrap object. If a bootstrap object is given then the intervals are bias corrected and the bootstrap variance estimate can be used if none is supplied.
Studentized: Studentized version of the basic bootstrap confidence interval.
Percentile: Bootstrap Percentile Confidence Interval Method. (they normalize it by Interpolation on the normal quantile scale. For a non-integer order statistic this function interpolates between the surrounding order statistics using the normal quantile scale. See equation 5.8 of Davison and Hinkley (1997)
I know that it's not much but I hope it helps a tiny bit.