Bias and variance reduction in estimating the proportion of true-null hypotheses

Bias and variance reduction in estimating the proportion of true-null hypotheses.

When testing a large number of hypotheses, estimating the proportion of true nulls, denoted by π(0), becomes increasingly important. This quantity has many applications in practice. For instance, a reliable estimate of π(0) can eliminate the conservative bias of the Benjamini-Hochberg procedure on controlling the false discovery rate. It is known that most methods in the literature for estimati...

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...

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 in Identifiable Nonparametric Models

A regression framework for the proportion of true null hypotheses

The false discovery rate is one of the most commonly used error rates for measuring and controlling rates of false discoveries when performing multiple tests. Adaptive false discovery rates rely on an estimate of the proportion of null hypotheses among all the hypotheses being tested. This proportion is typically estimated once for each collection of hypotheses. Here we propose a regression fra...