Calculate BCa Confidence Limits

DESCRIPTION:

Calculates BCa (accelerated bias-corrected) or BC (bias-corrected) bootstrap confidence limits.

USAGE:

limits.bca(boot.obj, probs=c(0.025, 0.05, 0.95, 0.975), 
           details=F, z0=NULL, acceleration=NULL, 
           group.size=NULL, frame.eval = <<see below>>, 
           subset.statistic=1:p, narrow=F) 

REQUIRED ARGUMENTS:

boot.obj
object of class .

OPTIONAL ARGUMENTS:

probs
probabilities for one-sided confidence limits; e.g. c(.025, .975) gives a two-sided 95% confidence interval. Note that values are undefined at 0 and 1.
details
logical flag indicating whether to return the values of z0, acceleration, group.size, and the adjusted probability levels for each BCa confidence limit along with the BCa limits. If details=F, only the BCa confidence limits are returned.
z0
bias-correction factor; by default this is estimated from the bootstrap results. It may also be calculated by .
acceleration
acceleration factor. By default this is estimated from the L component of boot.obj, if it is present, otherwise using . In the latter case, the statistic must allow samples of reduced size; see . It may also be calculated by .
group.size
number of observations to jackknife from each sample when calculating acceleration. It is time consuming to do a full delete-1 jackknife if n is large, so the default is to use a group size of floor(n/20), which yields roughly 20 groups of points, and hence 20 jackknife replicates. For the full jackknife, use group.size=1.
frame.eval
frame where the data and other objects used when creating boot.obj can be found. You need to specify this if objects can't be found by their original names, or have changed; see .
subset.statistic
subscript expression; if the statistic that was bootstrapped has length greater than 1, use this to request intervals for only some elements (parameters) of the statistic.
narrow
logical, determines how quantiles are computed. If narrow=FALSE (the default), then intervals are wider and coverage probabilities generally more accurate than with narrow=TRUE.

VALUE:

if details=F, returns a matrix of BCa confidence limits with one row per parameter of interest. Otherwise, returns a list with components:
limits
the BCa confidence limits.
z0, acceleration, emp.probs
quantities used in calculating BCa limits.

DETAILS:

If acceleration or z0 are large and requested probabilities are near 0 or 1, BCa limits are inaccurate, and may be ill-defined. If ill-defined the largest or smallest bootstrap replicate is returned. A warning about accuracy is provided if the adjusted probability levels and number of bootstrap replications are such that the limits are determined by a small number (currently 5) of the smallest or largest bootstrap replicates.

The values of z0 and acceleration estimated by and the acceleration value estimated by this function based on calling or using the L component of boot.obj assume that the bootstrap sample size is the number of observations in the original data -- i.e. that you are not using the size argument to the sampler passed to . Multiply those values by sqrt(n/size) to correct for the size argument.

This function assumes that boot.obj was created by ordinary bootstrapping, or something similar (the sampler argument to bootstrap could be samp.bootstrap, samp.boot.bal, or samp.bootknife, with size=n). If these assumptions are violated the intervals may be incorrect.

Bootstrap BC (bias-corrected) intervals can be obtained by setting acceleration=0.

z0 and acceleration should have length equal to the length of the observed component of boot.obj.

REFERENCES:

Davison, A.C. and Hinkley, D.V. (1997), Bootstrap Methods and Their Application, Cambridge University Press.

Efron, B. and Tibshirani, R.J. (1993), An Introduction to the Bootstrap, San Francisco: Chapman & Hall.

SEE ALSO:

, , , .

EXAMPLES:

temp <- bootstrap(stack.loss, var) 
limits.bca(temp) 
limits.bca(temp, details=T) 
 
infl <- influence(stack.loss, var) 
limits.bca(temp, z0 = infl$estimate$z0, 
           acceleration  = infl$estimate$acceleration)