Week 5 Flashcards
Def asymptotic normality
Required conditions for proving asymptotic Normality (1) for the MLE
Proving asymptotic normality using CLT
When θ^n is/looks like X— we can use CLT
Relate asymptotic normality to CRLB
n*Var(θ^) -> CRLB as n-> inf
Then θ^ is AE estimator of θ
Delta method
Delta method is considered a generalisation of CLT
Proof of Delta Method
Lecture 15
Is not examinable
Consistency of MME
Asymptotic normality of MME
This is essentially an implication of the delta method
MME
How and when does MME fail
For infinite expectation
Or
For E[X] is not a function of θ
Generalised MME
NOT EXAMINABLE
Required conditions for proving asymptotic distribution (2) for the MLE
How to check A6
Derivatives of integral = 0
As integral = 1
Therefore show that integral of deriv = 0
When asked about estimating a parameter that is an extremely complicated function of a parameter of a known dist
Appeal to invariance of MLE