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

[Antoine Monmayrant]

On 02/18/2014 03:06 PM, Yohann wrote:
> Hi all !!
>
> First of all, thank you to all contributors of Scilab.
> However, I have a problem to calculate the estimated error on each parameter
> calculated with leastsq.
>
> For example if I have the simple following function  to fit:
> !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
> function y = fun2fit(x, c)
>    y =  c(1)*x*x + c(2)*x + c(3);
> endfunction
>
> function e = myerror(c, x, y)
>    e = fun2fit(x, c) - y;
> endfunction
>
> // Data
> x = [ 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6]';
> y = [5.02  6.08  3.33 -0.93   -0.22  7.83  16.52 15.55  2.67 -11.42 -11.78
> 5.09 25.25]';
>
> // First guess
> c0 = [1 1 1]';
> y0 = fun2fit(x, c0);
>
> // least square
> [f, copt] = leastsq(list(myerror, x, y), c0)
> !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
>
> I'd like to have an estimated error on each of the 3 element of copt.
> Any idea ?
What do you mean?
Do you want a confidence interval or any kind of "error bar" for each 
parameter?
Or any way to see how your fit is dependent on each parameter?
If it's the case, you might be interested in bootstraping or 
jackknifing: http://en.wikipedia.org/wiki/Resampling_(statistics)
These methods are quite ressource hungry but work quite well to measure 
the quality and robustness of your fit.

Cheers,

Antoine
>
> Thanks !
> Y
>
>
>
>
>
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