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Re: st: basic question on nl


From   Muhammad Anees <anees@aneconomist.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: basic question on nl
Date   Mon, 7 Nov 2011 15:41:21 +0500

Sorry for being away from the discussion due to our Eid.

I agree with Nick in that I had assumed generalizations very specific
to Econometrics. Also, Nick is very clear in his statement. I apology
for my limiting the statement to Econometrics.

On Mon, Nov 7, 2011 at 3:27 PM, Nick Cox <n.j.cox@durham.ac.uk> wrote:
> 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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-- 

Regards
---------------------------
Muhammad Anees
Assistant Professor
COMSATS Institute of Information Technology
Attock 43600, Pakistan
www.aneconomist.com

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