Solution
= Solution
Scale cancels in
$$
T=\max_j\frac{|X_{1j}^TR|}{\|R\|}.
$$
Because $R=\sigma(I-P_0)Z$ under the null, it has exactly the requested distribution; its quantiles can be simulated without knowing $\sigma$.
= Solution
Scale cancels in
$$
T=\max_j\frac{|X_{1j}^TR|}{\|R\|}.
$$
Because $R=\sigma(I-P_0)Z$ under the null, it has exactly the requested distribution; its quantiles can be simulated without knowing $\sigma$.