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.