Selective Sign-Determining Multiple Confidence Intervals

• Activity Number: 563
• Type: Contributed
• Date/Time: Wednesday, August 6, 2014 : 2:00 PM to 3:50 PM
• Sponsor: Biopharmaceutical Section
• Author(s): Asaf Weinstein*+ and Daniel Yekutieli
• Companies: University of Pennsylvania and Tel Aviv University
• Keywords: Confidence Intervals ; Hypothesis Testing ; Multiplicity ; Three Decision Rule ; False Coverage Rate ; False Discovery Rate

Abstract

Given $m$ unknown parameters with corresponding independent estimators, the BH procedure can be used to classify the sign of parameters such that the proportion of incorrect directional decisions is controlled. More ambitiously, our goal is to construct sign-determining confidence intervals (CIs) such that the proportion of non-covering constructed intervals (FCR) is controlled. We suggest a valid procedure, which is governed by a choice of a marginal $1-\alpha$ CI. In particular, the shape of the marginal CI controls the tradeoff between the tendency to construct more confidence intervals (power) and the length of the constructed intervals. A one-sided marginal CI, for example, results in selecting according to a level-$2q$ BH procedure, but construct intervals of unbounded length; while using the two-sided marginal CI results in selecting according to a level-$q$ BH procedure, and in turn construct shortest CIs. We propose a new marginal CI that, when used in our procedure nicely balances this tradeoff. Specifically, we show in simulation that typically, it is possible to select according to BH at a level very close to $2q$ and at the same time construct short intervals.