Maximum Likelihood estimates follow a normal distribution

I was quite surprised when I learnt that a maximum likelihood estimate follows asymptotically a normal distribution with the mean being the estimated value and the variance being the inverse of the Fisher Information multiplied by the number of observations.

Asymptotically means when you have a big number of samples to calculate your ML estimate.

This is quite a remarkable fact. Some information: (page 10)

Haz clic para acceder a Fisher_info.pdf