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


From   "Verkuilen, Jay" <JVerkuilen@gc.cuny.edu>
To   <statalist@hsphsun2.harvard.edu>
Subject   RE: st: RE: Bootstrapping Conf Intervals - what do they mean?
Date   Tue, 3 Jun 2008 17:31:46 -0400

Salah wrote:

>>JV wrote:

"A 95% frequentist confidence interval says that 95% of such intervals
you gather will cover the true, fixed parameter"

If I understood you correctly, u are saying if one would repeat the
experiment 10000 times, 95% of these experiments would result in a
confidence interval that covers the unknown population estimate. I could
be missing something, but that does not seem to say much about the
current confidence interval: the one calculated from this data. How
likely that THIS confidence interval covers the true estimate?

First of all, I must say I hope I didn't get it backwards! The logic is
twisty. 

Anyway, one of the problems with the frequentist approach is the fact
that it seems odd that you can't make probability statements about the
thing you want to make inferences about, namely the parameter. What's
random is the sampling. Thus in the confidence interval, the only random
quantity is the parameter estimate (and its standard error). The
parameter is a fixed, but unknown quantity and thus we cannot make
probability statements about it. 

If this seems backwards to you and you want to say things like "there is
a 95% chance that the parameter lies in *this* interval", you're going
to have to break the Bayesian eggs. 

Jay

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