st: Re: ML estimation and gradient

[Kit Baum <baum@bc.edu>]

In any numerical optimization procedure with numerical derivatives,  
the derivative is an approximation to the slope along an  
infinitesimal segment of the function. If you took an arbitrarily  
small epsilon around the optimum, and the optimum was expressed to a  
precision beyond 15 digits, you would get something closer to zero.  
In something like -ml-, applying a tighter convergence criterion  
(i.e. the norm of the gradient must be no more than 10^-8) you may  
not find an optimum at all, or it may take a long time. Thus any  
optimization routine trades off precision for speed and likelihood of  
convergence. Stata's behavior in this regard is similar to that of  
any other software I have used.


Kit Baum, Boston College Economics and DIW Berlin
http://ideas.repec.org/e/pba1.html
An Introduction to Modern Econometrics Using Stata:
http://www.stata-press.com/books/imeus.html


On Aug 21, 2007, at 2:33 AM, statalist-digest wrote:


> I would like to know why, when using maximum likelihood estimation  
> in Stata,
>   the gradient in the last iteration is often numerically different  
> from
> zero whereas it should be theoretically equal to zero.
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