Simultaneous Critical Values for t-Tests in Very High Dimensions

• Activity Number: 79
• Type: Contributed
• Date/Time: Sunday, August 2, 2009 : 4:00 PM to 5:50 PM
• Sponsor: Biopharmaceutical Section
• Author(s): Hongyuan Cao*+ and Michael Kosorok
• Companies: The University of North Carolina at Chapel Hill and The University of North Carolina at Chapel Hill
• Keywords: multiple hypothesis testing ; microarrays ; high dimension ; one sample t-test ; two sample t-test ; self-normalized moderate deviation

Abstract

In micro array studies, image analysis, high throughput molecular screening, astronomy, and in many other high-dimensional contemporary statistical problems, hypothesis testing is applied in a simultaneous way. Popular alternatives to family wise error rate for calibration of multiplicity include k-family wise error rate (k-FWER), false discovery rate (FDR) and false discovery proportion (FDP). Most procedures in the literature are based on the assumption that the p-values of tests are known or that the distributions under both null and alternative hypotheses are known. However, these assumptions are generally not realistic. In this paper, we solve this problem for one-sample and two-sample t-statistics by developing a procedure to find valid critical values to control k-FWER, FDR and tail probability of FDP (FDTP).