Still on the mle command.
The argument of the mle command in gretl is actually the log-L
contributions and not the Log-L.
Clearly every combination of parameters that maximize the latter also
maximize the former.
So, as far as the point estimates of the parameters are concerned, it
does not really matters which one is used.
So far I have used mle simply as a maximization BFGS method, and I was
not looking at the covariance or the other ancillary statistics.
In my case working directly with the log-likelihood is much easier cause
I have a quite complex function that returns the SSR and I use it
directly in the command.
In case of homoscedastic normally distributed residuals, the Log-L is
indeed just:
Log-L = -n/2*(ln (ssr/n) + 1 + ln 2pi)
and I can use my function directly in the formula.
On the contrary, working directly with the log-L contributions is not
straightforward in my case.
I would like to know if I could use the covariance matrix and the other
statistics generated by the program (in particular the information
criteria), if, instead of using the Log-L contributions, I simply divide
the Log-L by n.
As far as the covariance is concerned, likely I cannot use the matrix
calculated from the outer product of the gradient, but can I use the
Hessian?
Thanks a lot
Giuseppe