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:

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:

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?