Selective Sign-Determining Multiple Confidence Intervals with FCR Control

Understand

Given $m$ unknown parameters with corresponding independent estimators, the Benjamini-Hochberg (BH) procedure can be used to classify the sign of parameters such that the expected proportion of erroneous directional decisions (directional FDR) is controlled at a preset level $q$.

• More ambitiously, our goal is to construct sign-determining confidence intervals---instead of only classifying the sign---such that the expected proportion of non-covering constructed intervals (FCR) is controlled.
• We suggest a valid procedure which adjusts a marginal confidence interval in order to construct a maximum number of sign-determining confidence intervals.
• We propose a new marginal confidence interval, designed specifically for our procedure, which allows to balance a trade-off between power and length of the constructed intervals, and, in fact, often enjoy (almost) the best of both worlds.