why MLE needs iteration to approximate the parameters?

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

[Torsten]

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]

What you said fully expressed my idea, Torsten.

Thank you for your supplement :)

Best regards,

Joy

Answer 1

[Matt J]

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.

[Joy Tian]

Perfect, Matt!

Thanks for further guidance. That is sooo helpful.

Best wishes,

Joy