Derive (16.67) using similar arguments to those leading to (16.66). Also establish the following results [see below (16.67)]:

(i) |tr(Σ
−1 −k ) − tr(Σ
−1)| ≤ 1;
(ii) |tr(Vk) − ptr(Σ
−1 ¯ UΣ
−1)| = OP(n).
(iii) (n − q)tr(Σ
−1 ¯ UΣ
−1 ¯U(1))
−→P ωd1.