There are a lot of problems that are solved by Maximum likelihood method. How to determine if the problem has a closed-form solution or not?


closed as too broad by kjetil b halvorsen, StasK, Xi'an, gung, John Oct 2 '15 at 16:25

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  • $\begingroup$ By trying? seeing? $\endgroup$ – kjetil b halvorsen Oct 2 '15 at 14:01
  • 3
    $\begingroup$ @kjetilbhalvorsen: I suppose the question's really how to distinguish between its not having one & your not having tried hard enough. $\endgroup$ – Scortchi Oct 2 '15 at 14:08
  • $\begingroup$ This strikes me as more of a general mathematical question, rather than anything statistics-specific. $\endgroup$ – gung Oct 2 '15 at 16:01

I doubt there is a rule here but in general this can be determined from the First Order conditions. If you end up having to solve non-linear equations, which cannot be simplified, then a numerical procedure is the way to proceed.


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