[RsR] [R] function in nls argument -- robust estimation

Hi Kate and Fernando,

I'm late into this thread,
but from reading it I get the impression that Fernando really
wants to do *robust* (as opposed to least-squares) non-linear
model fitting.  His proposal to set residuals to zero when they
are outside a given bound is a very special case of an
M-estimator, namely (if I'm not mistaken) the so-called "Huber
skipped-mean", an M-estimator with psi-function 
   psi <- function(x, k) ifelse(abs(x) <= k, x, 0)
It is known that this can be far from optimal, and either using
Huber-psi or "a redescender" such as Tukey's biweight can be
considerably better.
Also note that the standard inference (std.errors, P-values, ...)
that you'd get from summary(nlsfit) or anova(nls1, nl2) is 
*invalid* here, since you are effectively using *random* weighting.

The nlrob() function in package 'robustbase'
implements M-estimation of nonlinear models directly.
Unfortunately, how to do correct inference in this situation
is a hard problem, probably even an open research question in
parts. I would expect that "the" bootstrap should work if you only
have a few outliers.

I don't have time at the moment to look at the example data and
the model, and show you how to use it for nlrob();
if you find a way to you it for nls() , then the same should
work for nlrob().

I'm CCing this to the specialists for "Robust Stats with R"
mailing list, R-SIG-robust.

Best regards,
Martin Maechler
ETH Zurich