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

TLDR: In this paper, the problem of estimating the proportion of true null hypotheses, π0, i n a multiple-hypothesis set-up, is considered and the tests are based on observed p-values.

Abstract: Summary. We consider the problem of estimating the proportion of true null hypotheses, π0 ,i n 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 Spjotvoll. 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.