why MLE needs iteration to approximate the parameters?

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Joy Tian
Joy Tian 2015-7-24
评论： Joy Tian 2015-7-24
Hi Matlab fans,
I try to use mle function in Matlab to get the estimation of parameters.
I notice that in the syntax of mle , it requires to input the start-up guessing of parameters for the custom CDF.
Why? I remember in statistics class, my teacher said, to get the estimation from MLE, only partial derivatives of L function on each parameter is needed. If I substitute variables with corresponding sample value, I can obtain the values of parameters.
Can it be realized by Matlab?
Sincerely, Joy
  2 个评论
Torsten
Torsten 2015-7-24
The partial derivatives of the L function with respect to the unknown parameters are set to zero.
Then the resulting system of equations
dL/dp1 = 0
dL/dp2 = 0
...
dL/dp_n = 0
is solved for p_1,p_2,...,p_n.
This is usually a Newton-iteration which converges the better, the better the starting values.
Best wishes
Torsten.
Joy Tian
Joy Tian 2015-7-24
What you said fully expressed my idea, Torsten.
Thank you for your supplement :)
Best regards,
Joy

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采纳的回答

Matt J
Matt J 2015-7-24
编辑：Matt J 2015-7-24
only partial derivatives of L function on each parameter is needed.
That's true if the MLE has an analytical solution, which would often be the case in introductory MLE examples in a statistics course. More generally, though, a closed-form solution is not available and the maximizing parameters have to be found through iterative optimization.

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