I've noticed that in some places, the asymptotic variance of a Maximum Likelihood Estimator (MLE) under certain regularity conditions is listed as $\frac{1}{I(\Theta )}$.
However, it's also commonly listed as $\frac{1}{nI(\Theta )}$ in other texts. Why is the fisher information multiplied by $n$ in some contexts but not in others?
Example:
This question from stackexchange: Proof of asymptotic normality of Maximum Likelihood Estimator (MLE)
versus
Page 6 from these notes: https://ocw.mit.edu/courses/mathematics/18-443-statistics-for-applications-fall-2006/lecture-notes/lecture3.pdf