provide solution to all 4 parts

Q1 Consider a regression model Y =XB +E, where Yl1 Y12 1 X11 X12 811 812 Y21 Y22 1 X21 X 22 B10 B20 821 E 22 Y = X = B = B11 321 and 6 = . . . . . . B12 B22 Yni Yn2 1 Xn2 Enl En2 The elements s,; in s are iid from /(0, o2) with unknown o > 0. Define a loss function of B: n 2 L(B) = CE(Yjj - Bjo - XiBj - X12Bj2)?. 1=1 j=1 Derive an estimator 8 of 8 minimizing L(8). Show that 3 is the best linear unbiased estimator (BLUE). Find the joint distribution of the vectorized form of B. Construct a level a test for Ho : Bli = B21 and B12 = B22