Assumptions of SLRM
Invariance property of MLE
Consistency of a parameter
justifyMLE as point estimator
If a likelihood fx has unique maximum then
And this is the MLE
Score function
Gradient is taken WRT values of θ
(Strong) likelihood principle
Define the observed information matrix
Where p is dim of θ hence it becomes θ
How do you use score function and observed information matrix with MLE
MLE is solution to score function = 0
You can use the information matrix to determine if the inflection point is a maximum using second deriv