Week 5 Flashcards

1
Q

Def asymptotic normality

A
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
2
Q

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

A
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
3
Q

Proving asymptotic normality using CLT

A

When θ^n is/looks like X we can use CLT

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
4
Q

Relate asymptotic normality to CRLB

A

n*Var(θ^) -> CRLB as n-> inf

Then θ^ is AE estimator of θ

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
5
Q

Delta method

A

Delta method is considered a generalisation of CLT

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
6
Q

Proof of Delta Method

A
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
7
Q

Lecture 15

A

Is not examinable

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
8
Q

Consistency of MME

A
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
9
Q

Asymptotic normality of MME

A

This is essentially an implication of the delta method

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
10
Q

MME

A
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
11
Q

How and when does MME fail

A

For infinite expectation

Or

For E[X] is not a function of θ

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
12
Q

Generalised MME

A

NOT EXAMINABLE

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
13
Q

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

A
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
14
Q

How to check A6

A

Derivatives of integral = 0

As integral = 1

Therefore show that integral of deriv = 0

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
15
Q

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

A

Appeal to invariance of MLE

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
16
Q

Asymptotic efficiency

A

If an estimator is consistent and asymptotically normal