[R] Obtaining SE from the hessian matrix

[Timur Elzhov]

Dear R experts,

In R-intro, under the 'Nonlinear least squares and maximum likelihood
models' there are ttwo examples considered how to use 'nlm' function.
In 'Least squares' the Standard Errors obtained as follows:

    After the fitting, out$minimum is the SSE, and out$estimates are the
    least squares estimates of the parameters. To obtain the approximate
    standard errors (SE) of the estimates we do:

    > sqrt(diag(2*out$minimum/(length(y) - 2) * solve(out$hessian)))

But under 'Maximum likelihood' section I've read:

    After the fitting, out$minimum is the negative log-likelihood, and
    out$estimates are the maximum likelihood estimates of the parameters.
    To obtain the approximate SEs of the estimates we do:

    > sqrt(diag(solve(out$hessian)))

As for me, I use MINPACK fortran library for NLS fitting in R, and there
I also get the hessian matrix. What formula should I use in _this_ case?
Well, some times ago I had a glance at gsl, GNU Scientific Library. It
use converted-to-C MINPACK for NLS fit too.  And, in the GSL ref. manual
example
    http://www.gnu.org/software/gsl/manual/html_node/gsl-ref_36.html#SEC475
SE calculated as
    #define ERR(i) sqrt(gsl_matrix_get(covar,i,i))

where covar = (J^T * J)^-1 (i.e. how in the second formulae above).
So, what is the _right_ way for obtatining SE? Why two those formulas above
differ?

Thank you!

--
WBR,
Timur.