In the context of, show that for testing the LRT is a random monotone function of in (3.3.7). In, show that affin invariance implies (3.3.8), and as such, a best invariant test exists and is based...

In the context of, show that for testing

the LRT is a random monotone function of in

(3.3.7).

In, show that affin invariance implies (3.3.8), and as such, a best invariant test exists and is based on

in (3.3.7).

For the multi sample location model in, formulate the hypotheses (3.3.9) in an appropriate way and show that the Wald test is also a function of the classical ANOVA test.