Estimating the proportion of true null hypotheses under dependency: A marginal bootstrap approach

Abstract

Many estimators for the proportion of true null hypotheses in the literature, which are defined for independent p-values, struggle under dependence. In particular, the variance of the classical Schweder–Spjøtvoll estimator increases with the degree of dependence among the p-values. We propose a technique based on the independent-component bootstrap, which considerably improves this behavior. The idea of our marginal bootstrap modification is to utilize the conditional independence of the bootstrapped p-values and bagging to reduce the variance of the estimator. The theoretical validity of the resulting Bootstrap-Schweder–Spjøtvoll procedure is analyzed and its performance is illustrated on simulated data.