Under the random effects model (6.57), show that (a) SSA/SSR is maximal invariant under the group of transformations described in §6.3.2; (b) the UMPI test for XXXXXXXXXXderived in §6.3.2 is also a...

Under the random effects model (6.57), show that

(a) SSA/SSR is maximal invariant under the group of transformations described in §6.3.2;

(b) the UMPI test for (6.58) derived in §6.3.2 is also a UMPU test.

In Exercises 40 and 41 of §2.6, consider H0 : j = 1 versus H1 : j = 2.

(a) Derive the likelihood ratio λ(X).

(b) Obtain an LR test of size α in Exercise 40 of §2.6.