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

[Stéphane Mottelet]

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
>
>
>
> --
> View this message in context:
> http://mailinglists.scilab.org/evaluate-error-on-each-parameter-calculated-with-leastsq-tp4028696p4028748.html
> Sent from the Scilab users - Mailing Lists Archives mailing list archive
> at Nabble.com.
> _______________________________________________
> users mailing list
> users at lists.scilab.org
> http://lists.scilab.org/mailman/listinfo/users
>
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <https://lists.scilab.org/pipermail/users/attachments/20140220/4ca9c006/attachment.htm>