Exercise 9.10.10. In the multivariate linear model Y = XB+e the likelihood equations reduce to tr



Σ −1[dθ jΣ ]

+

= tr



Σ −1[dθ jΣ ]Σ −1Σˆ

+

, for j = 1, . . . , s where Σˆ ≡Y(I−M)Y/n and θ1,θ2, . . . ,θs from Chap. 4 correspond to σgh for g ≤ h so that s = q(q+1)/2.We recognize that Σ =Σˆ provides a solution to the likelihood equations. Now suppose that Σ ≡σ 2[(1−ρ)I1+ρJq q ], so that s=2 and (θ1,θ2)=(σ 2,ρ). It is clear that Σ =Σˆ still provides a solution to the likelihood equations, why is Σˆ no longer the MLE? (The argument has almost nothing to do with the particular parametric form that we chose for Σ .)