# What is the role of information matrix in Likelihood estimation?

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.

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