Roberto,
> What I do remember, however, is that you mentioned there that the
> bootstrap hadn't been investigated for the purposes of the maximum
> distribution in random fields.
That's right; the issue being that permutation methods are exact,
while Bootstrap methods are only asymptotic and need to be
investigated in each setting considered.
> I wonder if you went ahead with it.
Haven't done anything so far, mostly because of this paper [1], Troendle
et al. While this paper worked in microarrays and not smooth images,
they did do simulations in the small n, large number of tests setting, and
found that the Bootstrap was sometimes invalid, sometimes conservative,
depending on the resampling method; if you stick with the valid method,
you will have better power by going with thea permutation method (which
is exact). (I'd be happy to send a copy of the paper).
> We tried several bootstrapping schemes as part of our ADC map
> investigation, but I am not sure that if we wrote them up we would be
> reporting anything new.
If you found that the Bootstrap was useful for finding Familywise Error
(max-based) thresholds, then yes, it would be useful to report. It would
be useful because: (a) since the Bootstrap is only approximate, it needs
to be shown that it works in a given context, and (b) if only because
it contradicts existing work [1].
I look forward to seeing you results.
-Tom
[1] James F. Troendle; Edward L. Korn; Lisa M. McShane
An Example of Slow Convergence of the Bootstrap in High Dimensions
The American Statistician, 2004, vol. 58, no. 1, pp. 25 - 29
-- Thomas Nichols -------------------- Department of Biostatistics
http://www.sph.umich.edu/~nichols University of Michigan
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