Estimating the Proportion of True Null Hypotheses in Multiple Testing Problems

Estimating the Proportion of True Null Hypotheses for Multiple Comparisons

Whole genome microarray investigations (e.g. differential expression, differential methylation, ChIP-Chip) provide opportunities to test millions of features in a genome. Traditional multiple comparison procedures such as familywise error rate (FWER) controlling procedures are too conservative. Although false discovery rate (FDR) procedures have been suggested as having greater power, the contr...

Estimating the Proportion of True Null Hypotheses under Dependence

Multiple testing procedures, such as the False Discovery Rate control, often rely on estimating the proportion of true null hypotheses. This proportion is directly related to the minimum of the density of the p-value distribution. We propose a new estimator for the minimum of a density that is based on constrained multinomial likelihood functions. The proposed method involves partitioning the s...

On efficient estimators of the proportion of true null hypotheses in a multiple testing setup

We consider the problem of estimating the proportion θ of true null hypotheses in a multiple testing context. The setup is classically modeled through a semiparametric mixture with two components: a uniform distribution on interval [0, 1] with prior probability θ and a nonparametric density f . We discuss asymptotic efficiency results and establish that two different cases occur whether f vanis...

Towards Accurate Estimation of the Proportion of True Null Hypotheses in Multiple Testing

BACKGROUND Biomedical researchers are now often faced with situations where it is necessary to test a large number of hypotheses simultaneously, eg, in comparative gene expression studies using high-throughput microarray technology. To properly control false positive errors the FDR (false discovery rate) approach has become widely used in multiple testing. The accurate estimation of FDR require...

Estimating the Proportion of True Null Hypotheses in Identifiable Nonparametric Models