>A couple of weeks ago I made the following comments;
>unfortunately no-one followed it up
>(indeed my post seemed to kill the thread stone dead).
>I'd be grateful for defences of "bootstrap confidence intervals"
>(and discussion of other intervals generated by bootstrapping)
>-- not least because I'll be teaching bootstrapping next year!
>Please e-mail me, and I'll summarise to the net.
> -- Ewart Shaw
>===================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.
The theory behind the bootstrap certainly does _not_ assume (A). (Nor
does any other statistical theory of which I am aware.) Indeed, if
(A) were true then all features of the population could be learned
exactly from study of the sample. No probability theory, statistical
theory, or inferential methods would be needed. The bootstrap, in
particular would not be useful for inference, although resampling
might still be useful as a purely computational device.
Consistency ofa bootstrap statistic requires only that the sample
distribution converge (probabilitistically) to the population
distribution, and that the parameter of interest be a continuous
functional of the population distribution with respect to the metric
of convergence. Something more is needed for a bootstrap statistic to
have asymptotic performance superior to its "ordinary" counterpart.
-- T. Scott Thompson email: thompson@atlas.socsci.umn.edu Department of Economics phone: (612) 625-0119 University of Minnesota fax: (612) 624-0209