ABSTRACT
The parametric space O is the space {µ1,…, µk, S1,…, Sk)}, which reduces to the subspace ? ={(µ1,…, µk, S} under H0. The likelihood of the observations xij on Xij is
Using Lemma 5.1.1, a straightforward calculation will yield
When H0 is true the likelihood function reduces to
and
Thus the likelihood ratio test of H0 rejects H0 whenever
where the constant c is chosen so that the test has the required size a. From Section 6.3 it follows that the Si are independently distributed p×p a
Wishart random matrices with parameters Si and degrees of freedom Ni-1=ni (say). Bartlett, in the univariate case, suggested modifying ? by replacing Ni by ni and N
by (say).
