BCA method and alpha defaults

[mwort]

Hi @cgevans, thanks for this great scikit. I have questions regarding the implementation of the BCA method and the alpha argument to the ci function and I apologize if they might stem from an insufficient understanding of bootstrapping.

The bca method seems to take N+n_samples function evaluation rather than just n_samples, I believe because it calculates the jackknife mean with N function calls. This gets annoying if you have many empirical observations (e.g. N ~ n_samples). Efron and Tibshirani (1994)[0] state that their implementation uses "little more effort than for the percentile intervals" (p.178). A bit of a longshot but isnt there a way of reusing the previous evaluations?

And how come the percentiles default to alpha/2, 1-alpha/2 rather than just alpha, 1-alpha (e.g. as on E&T eq. 13.5, p.171)? Wouldn't typical 5-95% CI have an alpha of 0.05 (rather than 0.1)?

[0] https://books.google.de/books?id=gLlpIUxRntoC&lpg=PR14&ots=A9DxX6J6G6&dq=efron%20tibshirani%20bootstrap&lr&pg=PA171#v=onepage&q&f=false

[aizvorski]

@mwort "typical 5-95% CI" - I believe "95%CI" is 95% wide ie between 2.5% and 97.5%. Is there a reference that points to the other convention?

[cgevans]

@aizvorski It does appear that that part of Efron and Tibshirani uses $1-2\alpha$ for the percentile interval, not $1-\alpha$. The R boot package avoids confusion here by using conf instead of alpha as a parameter name.

A bit of a longshot but isnt there a way of reusing the previous evaluations?

I'm reasonably sure this isn't possible. E&T are likely saying that for the more usual case where $n_{samples} \gg N$.