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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.

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    $\begingroup$ There are so many posts pertaining to Information matrix here. What exactly do you need? $\endgroup$ Commented Dec 18, 2022 at 8:44
  • $\begingroup$ 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 $\endgroup$
    – Tatanik501
    Commented Dec 18, 2022 at 9:25
  • $\begingroup$ Hi: Below is a good introduction with possibly good references. andrewliao11.github.io/blog/fisher-info-matrix $\endgroup$
    – mlofton
    Commented Dec 18, 2022 at 13:26
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    $\begingroup$ Maybe this can help: What kind of information is Fisher information? $\endgroup$ Commented Dec 18, 2022 at 13:34
  • $\begingroup$ Thanks for your recommendations, I will check them. $\endgroup$
    – Tatanik501
    Commented Dec 19, 2022 at 8:09

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