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

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 tech...

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Bibliographic Details
Published in:Journal of statistical planning and inference 2021-01, Vol.210, p.76-86
Main Authors: Neumann, André, Bodnar, Taras, Dickhaus, Thorsten
Format: Article
Language:English
Subjects:
[formula omitted]-values
Bootstrap
Multiple testing
Schweder–Spjøtvoll estimator
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Summary: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. •We introduce a bootstrap version of the classical Schweder–Spjøtvoll estimator.•The proposed modification reduces the variance under dependency.•This is demonstrated theoretically and in simulations.•Source code and further supporting information is available for download.
ISSN:0378-3758
1873-1171
DOI:10.1016/j.jspi.2020.04.011