4. In the case r = 1, the statistic W given by (6) is maximal invariant under the group induced by G, and G3 on the statistics Y;, Va; (i = 1, . . . , p; IX = 1, . . . , S - 1), and S = Z'Z. [There exists a nonsingular matrix B such that B'SB = I and such that only the first coordinate of YB is nonzero. This is seen by first finding B, such that B(SB, = I and then an orthogonal Q such that only the first coordinate of YB,Q is nonzero.]