Week 6

Question 1

Is an unbiased estimator always consistent

Answer 1

No, apparently counter examples are hard to find

Var of N dist

Question 2

Def confidence interval

Answer 2

Question 3

Importance distinction for CI (maybe specific to frequentist interpretation)

Answer 3

Question 4

Asymptotic confidence interval

Answer 4

as n -> inf instead of equality

Where n is sample size

Question 5

Use the sample mean to form a standard Gaussian

Answer 5

Question 6

Combine χ^2 with sample mean to form student t

Answer 6

Question 7

Main difference between t and z when constructing CI

Answer 7

For Z we have a known var

Question 8

Not examinable from Lecture 17

Answer 8

Eg 3, cases 4 and 5 (pooled variance) CI

Question 9

How to think about confidence intervals

Answer 9

Introduce a dummy variable Y

Then sample n times and use indicator variable

Question 10

def pivotal quantity

Answer 10

A pivotal quantity in general is a function u(X; θ) of the observations X and the parameter θ that has a completely specified distribution F (·), that is, a distribution that does not involve any unknown parameters.