Week 6 Flashcards
Is an unbiased estimator always consistent
No, apparently counter examples are hard to find
Var of N dist
Def confidence interval
Importance distinction for CI (maybe specific to frequentist interpretation)
Asymptotic confidence interval
as n -> inf instead of equality
Where n is sample size
Use the sample mean to form a standard Gaussian
Combine χ^2 with sample mean to form student t
Main difference between t and z when constructing CI
For Z we have a known var
Not examinable from Lecture 17
Eg 3, cases 4 and 5 (pooled variance) CI
How to think about confidence intervals
Introduce a dummy variable Y
Then sample n times and use indicator variable
def pivotal quantity
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.