Statistica Sinica 30 (2020), 531-555

SELECTIVE SIGN-DETERMINING MULTIPLE

CONFIDENCE INTERVALS WITH FCR CONTROL

Asaf Weinstein and Daniel Yekutieli

Stanford University and Tel Aviv University

Abstract:
Given *m* berg (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.

Key words and phrases: Confidence intervals, directional decisions, false coverage rate, false discovery rate, selective inference, multiplicity.