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Building on [Prof. Matthew Stephens](http://stephenslab.uchicago.edu/)'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.