<p>I couldn't grasp what it refers to exactly so I would like to understand how we use it:</p>
<p>from MLE, Score Vector is:</p>
<p><span class="math-container">$$
S(\theta;y) = \frac{\partial l(\theta;y) }{\partial \theta} 
$$</span>
<span class="math-container">$l$</span> comes from the <strong>log</strong> version of the likelihood function and this score vector has an asymptotic distribution with Information Matrix which is:</p>
<p><span class="math-container">$$
I(\theta) = -E(\frac{\partial l(\theta;y) }{\partial \theta \partial \theta ^T } )
$$</span></p>
<p>I appreciate it if you can explain how to use it and which sources I can use.</p>

CC BY-SA 4.0
2022-12-17T01:58:05.927Z
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. https://www.amazon.com/s?k=jogesh+babu&crid=79Y6OHDJDOEA&sprefix=jogesh+babu%2Caps%2C76&ref=nb_sb_noss
mark leeds
CC BY-SA 4.0
2022-12-18T08:25:54.107Z
You may try asking questions like this on [Cross Validated](https://stats.stackexchange.com/questions) instead. You will find a larger pool of experts there.
Richard Hardy
CC BY-SA 4.0
2022-12-29T02:50:33.680Z
https://math.stackexchange.com/questions/4037394/covariance-matrix-inverse-and-second-order-derivatives-of-log-likelihood/4037862#4037862 Hope this helps.
Q9y5
<econometrics>
what is the role of information matrix in Likelihood estimation?
Tatanik501
# what is the role of information matrix in Likelihood estimation?

(Asked by: username_0 on 2022-12-16)

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.

**Tags:** econometrics

> **Comments:**
> **username_1**: 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. https://www.amazon.com/s?k=jogesh+babu&crid=79Y6OHDJDOEA&sprefix=jogesh+babu%2Caps%2C76&ref=nb_sb_noss  
> **username_2**: You may try asking questions like this on [Cross Validated](https://stats.stackexchange.com/questions) instead. You will find a larger pool of experts there.  
> **username_3**: https://math.stackexchange.com/questions/4037394/covariance-matrix-inverse-and-second-order-derivatives-of-log-likelihood/4037862#4037862 Hope this helps.  

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## 0 answers

