Week 5

Question 1

Def asymptotic normality

Answer 1

Question 2

Required conditions for proving asymptotic Normality (1) for the MLE

Answer 2

Question 3

Proving asymptotic normality using CLT

Answer 3

When θ^{^}_n is/looks like X^— we can use CLT

Question 4

Relate asymptotic normality to CRLB

Answer 4

n*Var(θ^) -> CRLB as n-> inf

Then θ^ is AE estimator of θ

Question 5

Delta method

Answer 5

Delta method is considered a generalisation of CLT

Question 6

Proof of Delta Method

Answer 6

Question 7

Lecture 15

Answer 7

Is not examinable

Question 8

Consistency of MME

Answer 8

Question 9

Asymptotic normality of MME

Answer 9

This is essentially an implication of the delta method

Question 10

MME

Answer 10

Question 11

How and when does MME fail

Answer 11

For infinite expectation

Or

For E[X] is not a function of θ

Question 12

Generalised MME

Answer 12

NOT EXAMINABLE

Question 13

Required conditions for proving asymptotic distribution (2) for the MLE

Answer 13

Question 14

How to check A6

Answer 14

Derivatives of integral = 0

As integral = 1

Therefore show that integral of deriv = 0

Question 15

When asked about estimating a parameter that is an extremely complicated function of a parameter of a known dist

Answer 15

Appeal to invariance of MLE

Question 16

Asymptotic efficiency

Answer 16

If an estimator is consistent and asymptotically normal