Bootstrap confidence intervals depend on three elements:

- the cdf of the bootstrap replications
- the bias-correction number which depends on the proportion of bootstrap estimates that are less than the original estimate
- the acceleration number that measures the rate of change in standard deviation of the estimate as the data changes.

The first two of these depend only on the bootstrap distribution, and not how it is generated: parametrically or non-parametrically. Therefore, the only difference in a parametric bca analysis would lie in the nonparametric estimation of the acceleration, often a negligible error.

The package `bcaboot`

provides functions to compute bootstrap confidence intervals in an (almost) automatic fashion. Further details may be found in the paper by Efron and Narasimhan below.

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References

Efron, Bradley, and Balasubramanian Narasimhan. The Automatic Construction of Bootstrap Confidence Intervals. (2018)