Let y ~ N,(1, o'1), where u and o' are unknown parameters. Let A, be the first n - 1 rows of I - H where H = 1(1*1)-11 and 1 is the n-dimensional column vector of ones. Also let A2 Set e = Ay. First show that the REML of o' is o? = et(AAt)-le/(n - 1). Then verify that o? = y*(I - H)y/(n -1). y1 - 1/2 (a) Let Z1 = Find the (n - 1) x n matrix A, such that Z2 = Aly and Un-1 - yn show that All = 0. (b) The reduced model corresponding to Ag is Z1 = Aly ~ N(0, 0?A2A; ), and the resulting REML of o' is given by of = z1(AlA;) 'z1/(n -1). Show that of = $2 where s' = _ _(yi - y)?/(n -1) is the sample variance estimator. y1 - y (c) Let z2 = 12 - y , where y = -_:Mi. Find the (n -1) x n matrix A2 such Un-1 - y that z2 = Azy. (d) The REML for o' corresponding to A2 is given by 0? = z2(A2A;)-1zz/(n -1). Show that of also coincides with $2