What is the role of information matrix in Likelihood estimation?

Asked Dec 18 '22 at 08:38

Active Dec 18 '22 at 08:42

Viewed 39 times

I couldn't grasp what it refers to exactly so I would like to understand how we use it:

from MLE, Score Vector is:

$$ S(\theta;y) = \frac{\partial l(\theta;y) }{\partial \theta} $$

$l$ comes from the log version of the likelihood function and this score vector has an asymptotic distribution with Information Matrix which is:

$$ I(\theta) = -E\left(\frac{\partial l(\theta;y) }{\partial \theta \partial \theta ^T } \right) $$

I appreciate it if you can explain how to use it and which sources I can use.

edited Dec 18 '22 at 08:42

User1865345

asked Dec 18 '22 at 08:38

Tatanik501

1

There are so many posts pertaining to Information matrix here. What exactly do you need? – User1865345 Dec 18 '22 at 08:44
I just can't understand what we did by taking this differentiation. But I guess it is related to the Variance of the Score vector – Tatanik501 Dec 18 '22 at 09:25
Hi: Below is a good introduction with possibly good references. https://andrewliao11.github.io/blog/fisher-info-matrix/ – mlofton Dec 18 '22 at 13:26
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Maybe this can help: What kind of information is Fisher information? – kjetil b halvorsen Dec 18 '22 at 13:34
Thanks for your recommendations, I will check them. – Tatanik501 Dec 19 '22 at 08:09
@Tatanik501 after reading them, you can update your post if you have any possible confusion (s) left. – User1865345 Dec 19 '22 at 08:14
Thank you sir, the first one is a quite impressive and smooth explanation. – Tatanik501 Dec 20 '22 at 07:35

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