Asymptotic theory for MLEs

Question 1

What does it mean to say an estimator is consistent?

Answer 1

pg 25

Question 2

What does it mean to say the MLE is asymptotically normal?

Answer 2

sqrt(n) (θ^ - θ_0) –d–> N(0, 1/I_{X_1}(θ_0) )

Question 3

Define asymptotically efficient

Answer 3

n var_{θ0} (θ^_n) –> I(θ0)^{-1}

Question 4

State the delta method, and write it out for dimension p=1

Answer 4

pg 28