Title | Simultaneous Critical Values For T-Tests In Very High Dimensions. |
Publication Type | Journal Article |
Year of Publication | 2011 |
Authors | Cao, Hongyuan, and Michael R. Kosorok |
Journal | Bernoulli (Andover) |
Volume | 17 |
Issue | 1 |
Pagination | 347-394 |
Date Published | 2011 Feb |
ISSN | 1350-7265 |
Abstract | 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. |
DOI | 10.3150/10-BEJ272 |
Alternate Journal | Bernoulli (Andover) |
Original Publication | Simultaneous critical values for t-tests in very high dimensions. |
PubMed ID | 21572564 |
PubMed Central ID | PMC3092179 |
Grant List | 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.
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