Functions
For the so called, BCa, interval, the approach requires an acceleration factor. The acceleration factor measures the rate of change of the standard error of the estimator with respect to the target parameter on a normalized scale. This function computes the acceleration factor based on the bootstrap estimates and the original estimated quantity using jackknifing: the sum of the cubed deviations of the jackknife replicates from their mean, divided by 6 times the 3/2 power of the sum of their squared deviations (Efron and Tibshirani, An Introduction to the Bootstrap, eq. 14.15). When the jackknife estimates do not vary, as for the median of data with many ties, there is no skewness to correct and the factor is 0.
For the so called, BCa, interval, the approach requires a bias correction factor which in essence measures the median bias of the bootstrap replicates for the estimated quantity. This function computes the bias correction factor based on the bootstrap estimates and the original estimated quantity. A bootstrap estimate equal to the original estimate counts as half below it, which keeps the factor finite for data with ties, as data from discrete inputs have. The factor is infinite only when every estimate lies strictly on one side of the original estimate.