Statistics 611
Homework #6 Solutions
Fall 2010
1. Note: All page numbers in this problem refer to the class notes for Chapter 5.
(a) Let K = G2 G1 . Then AKA = AG2 A AG1 A = A A = 0. Thus G2 = G1 + K
Statistics 611
Homework #5 Solutions
Fall 2010
= (I
1. (a) It follows from Problem 3 of Homework #3 that the vector of residuals is
XG11 X )y XG12 b, that E ( ) = 0, and that I XG11 X is symmetric an
Statistics 611
Homework #4 Solutions
Fall 2010
1. If x has a multivariate normal distribution N (, ), then its m.g.f. is
E [exp(t x)] = exp t +
1
t t
2
for t Rn .
Thus, for every n 1 vector of constan
Statistics 611
Homework #3 Solutions
Fall 2010
1. (a) For the unconstrained model, the regression line is E (y ) = 0 + 2 x for x t,
and is E (y ) = (0 + 1 ) + (2 + 3 )x for x > t. This regression has
Statistics 611
Homework #2 Solutions
Fall 2010
1. (a) Yes! If 1 and 2 are both estimable, then there exist vectors a1 and a2 such
that E (a1 y ) = 1 and E (a2 y ) = 2 , in which case E (a1 y + a2 y )
Statistics 611
Homework #1 Solutions
Fall 2010
1. (a) Part (i) of Corollary 1 to Lemma 1.4 follows from Lemma 1.4 and the corollary
to Lemma 1.1. Parts (ii) and (iii) are obtained by taking transposit