Before revision:  We justify this procedure under N, T \to \infty asymptotics where we allow T to be much smaller than N. As part of our theoretical arguments, we develop new simultaneous anti-concentration inequalities for the MAX and the QLR statistics.
After revision:  We justify our approach under N, T \to \infty asymptotics where we allow T to be much smaller than N. As part of our theoretical arguments, we develop new simultaneous anti-concentration inequalities for the MAX and the QLR statistics.