Estimating the proportion of true null hypotheses, with application to DNA microarray data

Mette Langaas, Bo Henry Lindqvist, Egil Ferkingstad

Journal of the Royal Statistical Society: Series B (Statistical Methodology) · 2005 · Volume 67 · Issue 4

DOI: 10.1111/j.1467-9868.2005.00515.x

Abstract

Summary.We consider the problem of estimating the proportion of true null hypotheses,π0, in a multiple-hypothesis set-up. The tests are based on observedp-values. We first review published estimators based on the estimator that was suggested by Schweder and Spjøtvoll. Then we derive new estimators based on nonparametric maximum likelihood estimation of thep-value density, restricting to decreasing and convex decreasing densities. The estimators ofπ0are all derived under the assumption of independent test statistics. Their performance under dependence is investigated in a simulation study. We find that the estimators are relatively robust with respect to the assumption of independence and work well also for test statistics with moderate dependence.

Keywords

Bioinformatics, Decreasing and convex density, Dependent test statistics, Multiple testing, Nonparametric maximum likelihood estimator, p-value

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