RE: st: basic question on nl

[Nick Cox <n.j.cox@durham.ac.uk>]

I guess it depends how strong the equivalence is. The flavour of the theorems is necessarily different given the very wide class of models being considered, with more arm-waving, or asymptotics, as I recall. If you want to cite theory you'll be best advised to trawl intermediate or advanced monographs; there are several suggestions in the -nl- manual entry. 

Nick 
n.j.cox@durham.ac.uk 

Sarah Kristina Reuter

Nick and Muhammad:

Thanks for your help. I'll try to get the book you recommended
Just want to add that I was aware of the fact that there are no linear estimators in nl, so they 
can't be BLUE. I was just wondering if there was an equivalent in nl to the BLUE theorem and 
conditions in linear regression. 

Am 6 Nov 2011 um 15:16 hat Nick Cox geschrieben:

> I partly agree with Muhammad. Most specifically, to echo what he
> says, there are no results for linear estimators, best or otherwise,
> in nonlinear least-squares models, quite simply because the
> estimators aren't linear. 
> 
> But whatever theorems there are in the literature don't buy you
> much. 
> 
> More generally, nonlinear least squares can work very well and very
> badly and not much is guaranteed. Your parameterisation, your
> starting points for estimation, and whether the model does fit at
> least roughly are important details. 
> 
> Muhammad seems to be presuming or implying that these models are
> specific to econometrics, which isn't correct. I imagine he would
> agree on reflection. They are used across science. Some of the
> fields in which they are very important include pharmacology,
> biochemistry and ecology and some of the best introductions to the
> topic I've come across are in those fields. 
> 
> Look at Amazon for books by Harvey Motulsky. 
> 
> Nick 
> n.j.cox@durham.ac.uk 
> 
> Muhammad Anees
> 
> BLUE has L for Linear while -nl- points to non-linear. Rest of the
> assumption should do the same job in both cases keeping basic
> econometric in mind. Non-linear estimation should also be Best,
> Unbiased and efficient estimator as a desire and need.
> 
> On Sat, Nov 5, 2011 at 10:20 PM, Sarah Kristina Reuter
> <sarah.kristina.reuter@uni-jena.de> wrote:
> 
> > What assumptions have to be met when performing a nonlinear least
> squares
> > (nl) regression?
> > In a linear LS-regression there are for example normally
> distributed and
> > uncorrelated errors, homoscedasticity and so on for the estimates
> to be
> > BLUE. Do the same assumtions hold in nl?
> > I've been checking some books but could find only the algorithms,
> not the
> > implicit assumptions...

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