Controlling the k-FWER by Adaptive Modified Bonferroni Methods under the Discrete Framework

Family wise error rate (FWER) is an important measure of the overall Type-I error when multiple tests are performed simultaneously. For a positive integer , -FWER is the probability of rejecting at least true null hypotheses. In this article, we present an adaptive version of the Bonferroni and the modified Bonferroni procedure for controlling -FWER by plugging-in an estimator of the proportion of true null hypotheses. We verify -FWER control of the adaptive methods empirically. Extensive simulation experiments exhibit the gain in power by the proposed methods over the existing methods for multiple discrete tests. We demonstrate applications of the proposed methods through two benchmark real-world datasets. IJSS, Vol. 24(2) Special, December, 2024, pp 123-136