V (r1,r1)
V (r2, r1)
V(r1,r2) . . . V(r1,rJ)
V(r2,r2) . . . V(r2,rJ)
V (rJ,r1)
V(rJ,r2) . . . V(rJ,rJ)
is positive semi-definite, where the latter matrix above is defined in the statement of Theo-
rem 1, part (i)b. Given Theorem 1, part (i)b, the statement follows directly.
(b) Immediate from Theorem 1, part (i)d.
In both cases, the unit asymptotic power of the proposed tests follows from Theorem 1, part
(ii).
28
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