# On the usage of numerical optimization technique to maximize log-likelihood

Literature and resources say that when the ML log-likelhood does not have a closed form expression, then we can use Newton-Raphson and other optimization techniques. My Question is:

During estimation of the ML estimator of an unknown parameter, upon taking the derivative of the log-likelihood and equating it to zero does not yield the estimator, then can we apply NR and other optimization techniuqes to solve the log-likelihood?

• Could you explain in what sense finding the critical points "does not yield the estimator"?
– whuber
Feb 3, 2015 at 21:16
• What I meant was that the parameter becomes zero say all the terms cancel out. Feb 3, 2015 at 21:28
• That sounds like a computational error on your part.
– whuber
Feb 3, 2015 at 21:29

• 1. one can use optimization methods even if it's not too complex, and even if it does have a closed form solution. $\:$ 2. I don't know for certain if there's another problem or not (I suspect so); it might indicate an algebraic error [or depending on exactly what the precise issue is, it might indicate a need for say l'Hôpital's rule or it might indicate something else (it might indicate something about the problem that you neglected to mention, for example). You should show the actual formula and the calculation for a more informed comment.] Feb 4, 2015 at 1:13