56. Under the assumptions of the preceding problem. the null distribution of W· is independent of q and hence the same as in the normal case. namely. F with r and n - s degrees of freedom. [See Chapter 5, Problem 24]. Note. The analogous multivariate problem is treated by Kariya (1981). who also shows that the test (9) of Chapter 8 continues to be UMP invariant provided q is a nonincreasing convex function. The same method shows that this conclusion holds under the same conditions also in the present case. For a review of work on spherically and elliptically symmetric distributions, see Chmielewski (1981).