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Re: Maximum likelihood and Mathematica


a) NMinimize[] and NMaximize[] do some kind of global optimization
b) but there is never a guarantee that a global extremum is found
    all methods for global optimization use heuristics that may work
    and find a global extremum or come close to the value of a global
c) giving good initial estimates may work better


snowrain wrote:
> I am doing MLE with Mathematica. When I put the parameters estimated from concentrated loglikelihood function into the gradient, the value is not close to zero. The command I used was "NMaximize". Does it only look for local maximum ? 
> When I estimate unconcentrated loglikelihood function, it shows error information that the loglikelihood is a complex number. There must be something wrong with the command that I am using since the concentrated and unconcentrated loglikehood functions should lead to the same estimate. 
> I found there is a package "Global Optimization" by Mathematica. Do I have to purchase and use it to find global optimization? And, why do I have different answers from the two loglikelihood functions? How can I check the steps/process of how Mathematica estimates the parameters? Thanks a lot !

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