Re: [Gretl-users] NLS stderr
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.
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