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From |
Roger Harbord <rmharbord@googlemail.com> |

To |
statalist@hsphsun2.harvard.edu |

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

Date |
Thu, 11 Feb 2010 16:41:53 +0000 |

As no-one has replied i'll attempt to wrap this up myself for the sake of posterity, based on a bit of further reading and a little further thought: I now think there's no point calculating acceleration factors in a sample this large and i'm safe to use bias-corrected (BC) confidence intervals rather than bias-corrected and accelerated (BCa) CIs. The acceleration factor 'a' is a second-order correction that goes as 1/sqrt(N), and with N=50000 the acceleration factor is of the order of 1/sqrt(50000) = 1/224, which is too small to matter. I was also confused about the role of skewness. The skewness of the jackknife estimates is used in computing the acceleration factor 'a'. But the fact that a bootstrap distribution is noticeably skew doesn't mean a bias-corrected and accelerated (BCa) confidence interval would differ noticeably from a bias-corrected (BC) interval, though it does mean that BC, BCa and percentile-based intervals will all differ noticeably from a normal-approximation interval, and the latter would have poor coverage. Roger. On Wed, Feb 10, 2010 at 5:59 PM, Roger Harbord <rmharbord@googlemail.com> wrote: > 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. > -- > Roger Harbord > http://www.epi.bris.ac.uk/staff/rharbord.htm * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**References**:**st: BCa bootstrap CIs: must I jackknife the entire sample?***From:*Roger Harbord <rmharbord@googlemail.com>

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