MoM and MLE

It's my last statistics class for my bachelor's degree, and my midterm is tomorrow, these are some resources I found for these concepts.

Method of Moments and Maximum Likelihood Estimation are two methods for estimating parameters of a distribution.


Basic Idea: equate sample moments with the respective theoretical moments E(X^k), k=1,2,3.... , until you have as many equations as parameters, and solve for the parameters.



Basic idea: maximize likelihood of data to estimate unknown parameter 𝛉. Find L(𝛉), log-likelihood it to make it easier to work with, differentiate it, set it to 0, and solve for 𝛉.


MoM vs MLE

MLEs can be shown to be asymptotically efficient, but MLEs require more assumptions. The best tool depends on the situation.

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