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st: BCa bootstrap CIs: must I jackknife the entire sample?

From   Roger Harbord <>
Subject   st: BCa bootstrap CIs: must I jackknife the entire sample?
Date   Wed, 10 Feb 2010 17:59:46 +0000

Dear Statalisters,

I have a dataset with fifty thousand observations, and a non-standard
estimation procedure for which i'd like to produce bias-corrected and
accelerated (BCa) bootstrap confidence intervals. My problem is that
the standard method of calculating the acceleration factor 'a'
requires jackknifing the entire dataset, i.e. calculating the estimate
leaving out each and every observation in turn, requiring fifty
thousand runs of my estimation procedure. I don't want to wait that
long and neither do my collaborators! To me it seems reasonable to
instead calculate 'a' from a random sample of leave-one-out estimates
- perhaps a thousand or more but far less than the whole fifty
thousand. Can anyone see any problems with this?

I can't believe i'm the first to come across this issue. Does anyone
know of any literature discussing this? (Unfortunately the potentially
relevant textbooks are on loan from our library at present, but i
haven't found anything relevant from an hour or so's perusal of
journal articles.) Is there any way of persuading the official
-bootstrap- command to do this, or am i going to have to knit my own?

And yes, i have examined the distribution of the bootstrap estimates
and in a few cases they are noticeably skew, even with this large a
sample, so i have reason for thinking BCa CIs could be a good idea.

Roger Harbord
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