|Simultaneous Critical Values For T-Tests In Very High Dimensions.
|Year of Publication
|Cao, Hongyuan, and Michael R. Kosorok
This article considers the problem of multiple hypothesis testing using t-tests. The observed data are assumed to be independently generated conditional on an underlying and unknown two-state hidden model. We propose an asymptotically valid data-driven procedure to find critical values for rejection regions controlling k-family wise error rate (k-FWER), false discovery rate (FDR) and the tail probability of false discovery proportion (FDTP) by using one-sample and two-sample t-statistics. We only require finite fourth moment plus some very general conditions on the mean and variance of the population by virtue of the moderate deviations properties of t-statistics. A new consistent estimator for the proportion of alternative hypotheses is developed. Simulation studies support our theoretical results and demonstrate that the power of a multiple testing procedure can be substantially improved by using critical values directly as opposed to the conventional p-value approach. Our method is applied in an analysis of the microarray data from a leukemia cancer study that involves testing a large number of hypotheses simultaneously.
|Simultaneous critical values for t-tests in very high dimensions.
|PubMed Central ID
|R29 CA075142 / CA / NCI NIH HHS / United States
R01 CA075142-11 / CA / NCI NIH HHS / United States
P01 CA142538-01 / CA / NCI NIH HHS / United States
R01 CA075142-10 / CA / NCI NIH HHS / United States
R01 CA075142 / CA / NCI NIH HHS / United States
R01 CA075142-09A1 / CA / NCI NIH HHS / United States
P01 CA142538 / CA / NCI NIH HHS / United States
Simultaneous Critical Values For T-Tests In Very High Dimensions.