I am taking an econometrics course and we are currently discussing Non-linear least squares (NLS). I have trouble understanding the asymptotic properties of Maximum likelihood estimation (MLE).
I have learned and understand MLE, but in my statistics course we never learned about a score or score function, an information matrix or asymptotic properties of MLE in general. Could someone recommend a good read or youtube channel that explained these concepts? I know some of these are answered on for example stack exchange, but my understanding of the subject is very low and I would like to start at lesson 1.
Some examples of things I would like to derive/proof myself:
$\sqrt(n)(\hat\theta-\theta) \rightarrow N(0, H^{-1}IHH^{-1})$
$plim(\frac{1}{n}H_n(\theta))=H_0(theta)$
$\frac{1}{\sqrt(n)} G_n(\theta_0) \rightarrow N(0, I_0)$