Hi,
On Sat, 12 Nov 2005 16:56:40 -0500 (EST)
Allin Cottrell <cottrell(a)wfu.edu> wrote:
> On Fri, 11 Nov 2005, Angelo Secchi wrote:
>
> > I'm playing a bit with the NLS command. I looked in the Manual for more
> > info about the stderr without success. Here my question.
> >
> > It seems to me that the stderr of the estimates are calculated as
> >
> > gradF*gradF^t
> >
> > Is that true? Is this the only way implemented?
>
> Sorry, this should be in the manual; I'll try to put it in shortly.
> The NLS covariance matrix (and coefficient standard errors) are
> calculated exactly as described in Davidson and MacKinnon,
> Econometric Theory and Methods, Chapter 6. See especially section
> 6.5.
thanks for the reference, I will check it.
> After the minpack miminizer is finished, we run the Gauss-Newton
> Regression (GNR) set out by D and M as equation (6.54), namely
>
> y - \hat{x} = \hat{X}b + residuals
>
> where \hat{x} is the vector of predictions from the NLS regression
> function and \hat{X} is the matrix of derivatives of the regression
> function with respect to the parameters. This is estimated via OLS,
> and the OLS covariance matrix from the GNR is used as the estimator
> of the variance of the NLS coefficients, Var(\hat{beta}).
>
> At present there is no provision to substitute an alternative
> estimator of Var(\hat{beta}), but I'm open to suggestions on that.
>
> Allin Cottrell
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Angelo Secchi PGP Key ID:EA280337
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Research Fellow Scuola Superiore S.Anna
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