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This approach is based on the fundamental principle of bootstrapping (Ref. 3):

1. Davison, A. C. and Hinkley, D. V. Bootstrap Methods and their Application, Cambridge University Press, 1997.

2. Efron, B. Bootstrap Methods: Another look at the jacknife, Ann. Statist. 7: 1-26, 1979.

3. Fox, J. and Weisberg, S. Bootstrapping regression models in R. An Appendix to An R Companion to Applied Regression, Second Edition (Sage, 2011). Revision as of 10 October 2017.

4. DiCiccio, T. J. and Efron, B. Bootstrap confidence intervals. Stat. Sci. 11: 189-228, 1996.

5. Canty, A. J., Davison, A. C., Hinkley, D. V., and Ventura, V. Bootstrap diagnostics and remedies. Can. J. Stat. 34: 5-27, 2006.

This approach is based on the fundamental principle of bootstrapping (Ref. 3):

1. Davison, A. C. and Hinkley, D. V. Bootstrap Methods and their Application, Cambridge University Press, 1997.

2. Efron, B. Bootstrap Methods: Another look at the jacknife, Ann. Statist. 7: 1-26, 1979.

3. Fox, J. and Weisberg, S. Bootstrapping regression models in R. An Appendix to An R Companion to Applied Regression, Third Edition (Sage, 2019). Revision as of 21 September 2018.

4. DiCiccio, T. J. and Efron, B. Bootstrap confidence intervals. Stat. Sci. 11: 189-228, 1996.

5. Canty, A. J., Davison, A. C., Hinkley, D. V., and Ventura, V. Bootstrap diagnostics and remedies. Can. J. Stat. 34: 5-27, 2006.

Should the percentile bootstrap never be used?

This behavior is nicely illustrated on this page, for bootstrapping a statistic so negatively biased that the original sample estimate is below the 95% CIs based on the empirical/basic method (which directly includes appropriate bias correction). The 95% CIs based on the percentile method, arranged around a doubly-negatively biased center, are actually both below even the negatively biased point estimate from the original sample!

Should the percentile bootstrap never be used?

Several issues can tends to make bootstrapped CIs unreliable. Some apply to all approaches, others can be alleviated by approaches other than the empirical/basic or percentile methods.

Several issues can tend to make bootstrapped CIs unreliable. Some apply to all approaches, others can be alleviated by approaches other than the empirical/basic or percentile methods.