Let e be the GLS estimator (4.22) under the assumptions (4.18) and (4.19). Assume that is known and 2 is fdunknown. Define the residual

Let e¯ be the GLS estimator (4.22) under the assumptions (4.18) and (4.19). Assume that §

is known and ¾2 is fdunknown. Define the residual vector e Æ Y ¡X e¯, and an estimator for ¾2

(e) Find E £
e¾
2 j X ¤
.
(f ) Is e¾
2 a reasonable estimator for ¾2?

02-11-82-18 n-k (a) Show (4.23). (b) Show (4.24). (c) Prove that = Me, where M = 1-X (X'X)X' (d) Prove that M'EM = 2-1-2-x(x'-1x)x'-1.