I am interested whether you know any distributions or special cases where the maximum likelihood estimator, the theoretical and estimated asymptotic variance can be fully derived manually, i.e. which have a closed form solution and we do not need numerical tools. The derivation should not be too demanding, say an average person who is familiar with maximum likelihood should solve it in $<1/2$ hour.
I did some research on it and already derived for the following pdf's:
- Poisson
- Binomial
- Gaussian
- Exponential
- Linear regression (assuming normal distribution of the error term + some more assumptions)
Any input and advice is welcome. Also references where people already made a collection on that topic would be great.