Week 7

Question 1

How to prove asymptotic normality?

Answer 1

Use CLT or Delta method

Question 2

Prove consistency using?

Answer 2

Weak LLN

Question 3

We say to rvs X and Y are identically distributed if

Answer 3

And only if

Question 4

Elimination of parameters

Answer 4

We can’t integrate out nuisance parameters
Because parameters are unknown BUT fixed quantities therefore we can’t integrate them out of the likelihood function

But should only deal with one parameter at a time

However in Bayesian stats, params are RVs

Question 5

Profile likelihood

Answer 5

(Also called relative likelihood)
Alternative to elimination of parameters

Question 6

Willk’s Theorem

Answer 6

Example included

Question 7

Relative likelihood function

Answer 7

If a model contains only one parameter then R(θ | x) is RLF

Question 8

Wald CI

Answer 8