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 _______________________________________________ Gretl-users mailing list Gretl-users(a)ricardo.ecn.wfu.edu http://ricardo.ecn.wfu.edu/mailman/listinfo/gretl-users