A sequence (epsilon_{v} ightarrow 0) such that (P_{u}left(|X| epsilon_{u} mid Yight)=frac{ho zeta(y)}{1-ho+ho zeta(y)}+o(1) ] which implies that the 'true discovery rate' is essentially independent of

A sequence \(\epsilon_{v} ightarrow 0\) such that \(P_{u}\left(|X|<\epsilon_{v}ight) ightarrow 1\) as \(v ightarrow 0\) is called a signal negligibility threshold. Show that the conditional probability of a non-negligible signal is

\[
P_{u}\left(|X|>\epsilon_{u} \mid Yight)=\frac{ho \zeta(y)}{1-ho+ho \zeta(y)}+o(1)
\]

which implies that the 'true discovery rate' is essentially independent of the threshold.