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Maximum likelihood and Mathematica

• To: mathgroup at smc.vnet.net
• Subject: [mg85252] Maximum likelihood and Mathematica
• From: snowrain <anne_xuetulip at hotmail.com>
• Date: Mon, 4 Feb 2008 03:13:53 -0500 (EST)
• Organization: The Math Forum

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 !