Calculation of the Standard Error of Parameters in non-linear Regression

• Oct 14th 2011, 11:11 AM
Boojakascha
Calculation of the Standard Error of Parameters in non-linear Regression
Hello

Today I recreated an estimation of standard error for a parameter analytically. I compared it with the standard Error traced by Mathematica and it is for two examples quite different.
The two examples were:
$y = x \cdot e^{p}$

$y = x^{p}$

Because of this I recalculated in a program which does the estimation numerically (gnuplot). The traced value is very similar to the one by Mathematica. So my question: Does it Mathematica just numerically?

I used the analytical procedure usual in Newton-Gauss procedure:
$\sigma_{pi} = \sigma_{r} \cdot \sqrt{inv(H)_{i,i}}$
Where H is the Hess matrix

I know this method is just a estimation, but a analytical method should be general better than anything numerical, am I right?
• Oct 14th 2011, 11:20 AM
CaptainBlack
Re: Calculation of the Standard Error of Parameters in non-linear Regression
Quote:

Originally Posted by Boojakascha
Hello

Today I recreated an estimation of standard error for a parameter analytically. I compared it with the standard Error traced by Mathematica and it is for two examples quite different.
The two examples were:
$y = x \cdot e^{p}$

$y = x^{p}$

Because of this I recalculated in a program which does the estimation numerically (gnuplot). The traced value is very similar to the one by Mathematica. So my question: Does it Mathematica just numerically?

I used the analytical procedure usual in Newton-Gauss procedure:
$\sigma_{pi} = \sigma_{r} \cdot \sqrt{inv(H)_{i,i}}$
Where H is the Hess matrix

I know this method is just a estimation, but a analytical method should be general better than anything numerical, am I right?

No, depends on the approximation in the analytic method, there will always be cases where a particular approximation falls down. The numerical method will be something like the Jackknife (or if the problem is suitable the Bootstrap) and should be fairly robust.

CB