Building on Prof. Matthew Stephens’s insight that under correlation, the empirical distributions of the observations are different from their theoretical one. However, correlation affacts observations unequally. Moderate observations, defined as \(|\hat\beta / \hat s| \leq t\) with a pre-specified \(t\), are more prone to correlation and thus contain less information to control false discoveries than extreme ones, truncash makes partial use of moderate observations, combined with full use of extreme ones, to adaptively shrink the measurements with heteroskedastic noise.

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