Mathematics – Statistics Theory
Scientific paper
2011-02-10
Bernoulli 2011, Vol. 17, No. 1, 347-394
Mathematics
Statistics Theory
Published in at http://dx.doi.org/10.3150/10-BEJ272 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statisti
Scientific paper
10.3150/10-BEJ272
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 the $k$-familywise 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 a 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.
Cao Hongyuan
Kosorok Michael R.
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