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

  1. #1
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    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?
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  2. #2
    Grand Panjandrum
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    Re: Calculation of the Standard Error of Parameters in non-linear Regression

    Quote Originally Posted by Boojakascha View Post
    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
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