Estimating the Proportion of True Null Hypotheses, with application to DNA Microarray Data

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 observed p-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 the p-value density, restricting to decreasing and convex decreasing densities. The estimators of π0 are 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.