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st: RE: Bootstrapping Conf Intervals - what do they mean?


From   "Verkuilen, Jay" <JVerkuilen@gc.cuny.edu>
To   <statalist@hsphsun2.harvard.edu>
Subject   st: RE: Bootstrapping Conf Intervals - what do they mean?
Date   Tue, 3 Jun 2008 16:42:03 -0400

Dan Weitzenfeld wrote:

>>I'm grappling with what the results of Bootstrapping can tell you.
Let's say I bootstrap from my sample 10,000 times, calculating a given
statistic, giving me the detail I need to use the 2.5% and 97.5%
percentiles to construct a 95% confidence interval. What does that
*mean*? Am I 95% confident that the true value of that statistic is
within the interval?  <

<Bayesian> A bootstrap interval means the same bass-ackwards thing as
any other frequentist interval estimate.</Bayesian> 

In short, you've got it backwards. A 95% frequentist confidence interval
(gotten however you got it, either from asymptotics or bootstrapping)
says that 95% of such intervals you gather will cover the true, fixed
parameter. The parameter is an unknown but fixed constant. The intervals
are random. 


>>If so, doesn't that require 100% confidence that my sample is an
accurate representation of the underlying population?<<

The validity of any inferential procedure depends on your having a good
sample, or a way to model the sampling situation, as is the case with
censored data, sample selection models (Heckman) and the like. 

JV

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