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RE: st: basic question on nl


From   Nick Cox <n.j.cox@durham.ac.uk>
To   "'statalist@hsphsun2.harvard.edu'" <statalist@hsphsun2.harvard.edu>
Subject   RE: st: basic question on nl
Date   Sun, 6 Nov 2011 15:16:08 +0000

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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