[Scilab-users] evaluate error on each parameter calculated with leastsq

[Stéphane Mottelet]

Here is a simple example where the derivative is approximated with the
"derivative" macro of Scilab.

S.


2014-02-20 9:43 GMT+01:00 Stéphane Mottelet <stephane.mottelet at gmail.com>:

> Hello,
>
> If you can make the hypothesis that your data is corrupted by gaussian
> noise, then you can approximate the covariance matrix of your estimated
> parameters. Let p be the vector of parameters and r(p) the residual vector
> given by
>
> r(p)=sigma^(-1)*(y-Y(p))
>
> where y is your measuement vector, Y(p) the "simulated" measurement, sigma
> a diagonal matrix with the std error for each measurement. If we denote by
>
> drdp(p) the derivative (or jacobian matrix) of r with respect to p then
> the covariance matrice C of parameters can be estimated by
>
>
> C=F^(-1)
>
> where
>
> F=drdp(p)' * drdp(p)
>
> is the Fisher information matrix. The diagonal terms of V give you the
> variance of the parameters. Of course, even in the gaussian case, this is a
> crude approximation....
>
> S.
>
>
> 2014-02-19 17:10 GMT+01:00 Yohann <yohann.morille at univ-angers.fr>:
>
> yes I know Denis, It was just an example to illustrate my question.
>> My real dataset and function to fit are completely different and more
>> complex.
>> Thank you
>>
>>
>>
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