Selective sign-determining multiple confidence intervals with FCR control

Given m unknown parameters with corresponding independent estimators, the Benjamini–Hochberg (BH) procedure can be used to classify the signs of the 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 noncovering constructed intervals (FCR) is controlled. We suggest a valid procedure that adjusts a marginal confidence interval to construct a maximum number of sign-determining confidence intervals. We propose a new marginal confidence interval, designed specifically for our procedure, that allows us to balance the trade-off between the power and the length of the constructed intervals. We apply our methods to detect the signs of correlations in a highly publicized social neuroscience study and, in a second example, to detect the direction of association for SNPs with Type-2 diabetes in GWAS data. In both examples, we compare our procedure to existing methods and obtain encouraging results.