Lecture 6

Question 1

What is theorem 26 (Lindeberg-Feller CLT)? What is one critical assumption?

Answer 1

Question 2

What are thre assumptions needed for the Lindeberg-Feller CLT to hold?

Answer 2

Question 3

The Lindeberg condition is important to the CLT. By which assumption can we change it?

Answer 3

Question 4

What is theorem 28.

Answer 4

With the assumptions:
1. {ui} is independent with Eui = 0 and Eui = sigma^2 and {ui^2} is UI

2. {zi is non stochastic adn satisfies the Grenander’s conditions.

Question 5

What is Cramer’s Theorem?

Answer 5

Question 7

We have that for theorem 28 to hold, we must have that:
1. {ui} is independent with Eui = 0 and Eui = sigma^2 and {ui^2} is UI

2. {zi is non stochastic adn satisfies the Grenander’s conditions.

By which conditions can these two conditions be replaced by? What do they imply?

Answer 7

If {ui} is iid (0, sigma^2) (Because iid with finite second moment implies that {ui^2} is UI)
and if zij = i^p with p>-1/2.

It implies that our parameter converges to a normal k distribution even if we admit trends in the data as long as the variance of the error term is UI.