Robust Non-linear Regression

Hi,

I'm trying to use Robust non-linear regression to fit dose response  
curves.
Maybe I didnt look good enough, but I dind't find robust methods  
for NON
linear regression implemented in R. A method that looked good to me  
but is
unfortunately not (yet) implemented in R is described in
http://www.graphpad.com/articles/RobustNonlinearRegression_files/ 
frame.htm
<http://www.graphpad.com/articles/RobustNonlinearRegression_files/ 
frame.htm>


in short: instead of using the premise that the residuals are  
gaussian they
propose a Lorentzian distribution,
in stead of minimizing the squared residus SUM (Y-Yhat)^2, the  
objective
function is now
SUM log(1+(Y-Yhat)^2/ RobustSD)

where RobustSD is the 68th percentile of the absolute value of the  
residues

my question is: is there a smart and elegant way to change to  
objective
function from squared Distance to log(1+D^2/Rsd^2) ?

or alternatively to write this as a weighted non-linear regression  
where the
weights are recalculated during the iterations
in nlme it is possible to specify weights, possibly that is the way  
to do
it, but I didn't manage to get it working
the weights should then be something like:

SUM (log(1+(resid(.)/quantile(all_residuals,0.68))^2)) / SUM (resid 
(.))

the test data I use :
x<-seq(-5,-2,length=50)
x<-rep(x,4)
y<-SSfpl(x,0,100,-3.5,1)
y<-y+rnorm(length(y),sd=5)
y[sample(1:length(y),floor(length(y)/50))]<-200 # add 2% outliers  
at 200

thanks a lot

Hans Vermeiren


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