Consider the model, defined by the following assumptions:

Show that under usual assumptions (A1)(A4), the OLS estimator is the Best Linear Unbiased Estimator

(BLUE) of , where best means having the smallest variance, i.e. the Gauss-Markov Theorem.

Now we have the following estimator for ²: 2(sigma hat^2) = I=1n(Y_i X_i^(hat))² = n¹UU.

Show that under usual assumptions (A1)(A4), ²(sigma hat²) is a biased estimator. Propose an unbiased estimator of ².

Now we have additional assumptions: A6: {(Yi,Xi):i =1,...,n}iid, A7 : E(Xi Xi) is a positive definite matrix.

f) Show that under assumptions (A1),(A2),(A6) & (A7), the OLS estimator is consistent, i.e. _n(hat) p as n .