Assume that the model y = Xβ + u satisfies the Gauss-Markov assumptions and let be the OL...

Assume that the model y = Xβ + u satisfies the Gauss-Markov assumptions and let be the OLS estimator of β. Let Z = G(X) be an n × (k + 1) matrix function of × and assume that ZʹX [a (k + 1) × (k + 1) matrix] is nonsingular. Define a new estimator of β by = (ZʹX)1Zʹy.

(i) Show that E( X) , so that is also unbiased conditional on X.

(ii) Find Var( X). Make sure this is a symmetric, (k + 1) × (k + 1) matrix that depends on Z, X, and σ2.

(iii) Which estimator do you prefer, or ? Explain