past papers

Question 1

what is a hypothesis

Answer 1

a hypothesis is a statement about a model parameter

Question 2

Define observed information for 1 single param

Answer 2

Question 3

What is a sufficient statistic

Answer 3

Question 4

Def profile likelihood

Answer 4

Question 5

Def 1 sided hypothesis test

Answer 5

Question 6

Def marginal likelihood in Bayes theorem

Answer 6

Question 7

Find minimal sufficient stat

Answer 7

Identity pdf
Identify joint pdf
Apply factorisation theorem (find h(x) that doesn’t depend on θ)

Then for minimal

Question 8

When finding fisher information remember to

Answer 8

Switch to single variable case

Question 9

Method of moments

Answer 9

Where moments are acquired/given earlier

Question 10

Prove consistency

Answer 10

Use LLN (+CMT if necessary)

Question 11

LLN

Answer 11

Sn

Question 12

Difference between strong and weak LLN

Answer 12

If mean is finite => weak (converges in P to μ)
If mean AND var is finite => strong (a.s coverages to μ)

Question 13

Bayes theorem

Answer 13

Question 14

When determining conjugate prior remember to

Answer 14

Only include the kernel of the distribution

Question 15

When asked about n -> inf

For bayesian point estimator

Answer 15

Divide through by n to see dominant terms

Question 16

Def pivotal quantity

Answer 16

A function of the observation and the parameters for which the distribution is entirely specified

Question 17

Showing that a quantity is pivotal

Answer 17

Show that it’s distribution doesn’t depend on the parameter of interest

Question 18

Power and size of test

Answer 18