(BHHH) Consider the optimization of the multivariate normal log-likelihood function

(a) How can this log-likelihood be maximized over $\mu$ and $\Omega$ without numerical optimization algorithms?

(b) Will a single iteration of such quadratic algorithms as BHHH yield the optimum?

(c) Suppose that the number of observations N is less than the number of parameters in $\mu$ and $\Omega$. Show that the BHHH algorithm will break down because its approximation to the Hessian is singular, whereas the other quadratic approximations will generally work. Can you suggest a way to help overcome this problem with BHHH?

Ex [Z (p. 92: y)] = log det $2 2 Exly ) (y-p)]