Hey ho. This falls into a common trap of assuming that the bootstrap
gives samples from the original distribution. It does not, by any means.
In this case the original sample will (I hope) have distinct values, the
bootstrap lots of repeated values. Most spline smoothing code does not
handle repeated values well (you don't say which one you are using) and in
any case the problem is nothing like the original one; for example
the distinct points are on average farther apart. I suspect that
the optimal degree of smoothing for a bootstrap re-sample is considerably
larger than for the original sample, as the effective sample size for the
re-sample really is much smaller.
My understanding is that the bootstrap assesses \hat\theta - \theta
by looking at \theta^* - \hat\theta (and often does that in very
complicated ways). So in this problem you need to compare results
on bootstrap resamples under both x and y df, _and_ you need some theory
to demonstrate that the resampling biases are of a high enough asymptotic
order.
Trust me (as Bill V says), you really don't want to try to prove such
a procedure works. And it is vastly slower than AIC.
-- Brian D. Ripley, ripley@stats.ox.ac.uk Professor of Applied Statistics, http://www.stats.ox.ac.uk/~ripley/ University of Oxford, Tel: +44 1865 272861 (self) 1 South Parks Road, +44 1865 272860 (secr) Oxford OX1 3TG, UK Fax: +44 1865 272595 ----------------------------------------------------------------------- This message was distributed by s-news@wubios.wustl.edu. To unsubscribe send e-mail to s-news-request@wubios.wustl.edu with the BODY of the message: unsubscribe s-news