# 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:

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

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

• hi: you'd have to read a fairly advanced book on statistical inference. one recommendation is this one at the link below. there are probably other good ones that I am not aware of so hopefully other recommendations will follow from others. amazon.com/… Dec 17, 2022 at 1:58
• You may try asking questions like this on Cross Validated instead. You will find a larger pool of experts there. Dec 18, 2022 at 8:25
• math.stackexchange.com/questions/4037394/… Hope this helps.
– Q9y5
Dec 29, 2022 at 2:50