Re: Bootstrap confidence intervals
Karl W Broman (kbroman@gandalf.Berkeley.EDU)
Fri, 29 Jul 94 12:49:18 EDT
>
>===================ORIGINAL COMMENTS FOLLOW=========================
>The idea of using the bootstrap to obtain CI's has always
>struck me as perverse, since one is simultaneously assuming:
>
>(A) (for bootstrapping) The underlying population distribution is
> precisely the same as the observed sample distribution.
>
>(B) (to get a CI) The underlying population distribution is not
> necessarily the same as the observed sample distribution.
>
>If you add to (A) "...except for a location shift",
>then there is no non-zero shift that would make any other
>population distribution compatible with the observed data
>(unless, for example, you have observed some data at all integer
>values, and are only considering possible integer location shifts!)
>
>I suspect this is at bottom a criticism of CI's, not of the bootstrap.
>======================================================================
>--
>J.E.H.Shaw, Department of Statistics, | JANET: strgh@uk.ac.warwick
> University of Warwick, | BITNET: strgh%uk.ac.warwick@UKACRL
> Coventry CV4 7AL, U.K. | PHONE: +44 203 523069
>An ex-algebraist who lost his ideals, his associates, and finally his identity
I don't agree with your points.
It is my understanding that the assumption made in a bootstrap
is basically that the sorts of errors made in inferring from a sampled
sample to the sample (errors that we can see) are similar to the sorts
of errors made in inferring from the sample to the population (errors
that we can't see).
It is not necessary that the distributions be the same, though
certainly that is sufficient. Of course, the behavior of the
bootstrap depends greatly on what you are estimating!
One may obtain additional information about the quality of
one's inference by performing a second level of bootstrapping:
considering the distribution of one's estimates for the sampling of
the sampled samples, or whatever.
karl
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karl w. broman 734 alcatraz av., #2
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kbroman@stat.berkeley.edu (510) 658-2544
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